WASHINGTON -- Republican presidential candidate Mitt Romney's frequent remarks about the nation's unemployment problem have long included one curiosity, if not an outright contradiction: It's bad for private-sector workers to lose their jobs, he says, but it's often good for government workers to do so.

Romney's positions on employment are drawing new attention after his back-to-back comments about firefighters, police officers and teachers. The nation doesn't need more of these workers, Romney said last Friday. And the federal government doesn't pay for them, he said Tuesday, after Democrats harshly criticized him.

The first statement can be debated. The second claim is simply false because the federal government spends billions of dollars a year to pay for teachers, police officers and firefighters throughout the country.

It's true that local governments generally hire such workers. But they use a mix of local, state and federal money to pay them. Romney would have been on firmer ground had he said the federal government doesn't "hire" teachers, police and firefighters.

What's clear is that U.S. communities would have fewer such public-sector workers if the federal government stopped funding teachers through Title I, police officers through the COPS program and firefighters through the SAFER program.

Romney sometimes suggests that firing a government employee can directly lead to the hiring of one or more private-sector workers. He told Colorado voters last month that President Barack Obama's stimulus program "didn't help private-sector jobs. It helped preserve government jobs."

The place to cut back, Romney said, "was on government jobs. We have 145,000 more government workers under this president. Let's send them home and put you back to work."

Numerous independent economists have said the stimulus prevented the economic collapse, including private and public-sector jobs losses, from being worse.

As for any increase in government employment since Obama took office in January 2009, that is true only if it refers solely to federal workers, and many of those were hired in areas Romney supports, such as the military and veterans' affairs.

Meanwhile, hundreds of thousands of state, county and municipal workers have been laid off as local governments cope with ailing economies and decreased federal aid. The Bureau of Labor Statistics says 607,000 government jobs – all of them nonfederal – have been lost since January 2009.

From a statistical standpoint, a laid-off government worker adds one name to the unemployment rolls, just as a laid-off private worker does. Economists and partisans debate the degree to which a smaller bureaucracy can lead to lower taxes, and perhaps less regulation, which might spur private expansion and hiring.

The latest back-and-forth over Romney's remarks began Friday. That morning, Obama, trying to note the difference between private-sector job losses and nongovernment job growth, told reporters "the private sector is doing fine."

The private sector has added 847,000 jobs so far this year. But Obama's phrasing made him sound out of touch with Americans' anxiety, and Romney was among those who pounced.

Obama "wants to hire more government workers," Romney said in Iowa, alluding to neighboring Wisconsin, where GOP Gov. Scott Walker had just triumphed in a recall election triggered by his attacks on public-sector employee unions. "He says we need more firemen, more policemen, more teachers. Did he not get the message in Wisconsin? The American people did. It's time for us to cut back on government and help the American people."

Democrats, eager to change the subject from the president's verbal misstep, counterattacked. Obama campaign spokesman Ben LaBolt said Romney was "calling for further job loss in the sector that needs the most urgent boost."

Other Democrats noted the federal role in putting teachers in schools and police on the streets. Title I funding for school personnel was $14.5 billion this year, the Senate Appropriations Committee said. Federal grants to states for special education reached $11.5 billion.

Millions of federal dollars put police and firefighters in various communities.

On Fox News on Tuesday, Romney rejected claims that his policies would worsen unemployment and deprive communities of needed services.

"Teachers and firemen and policemen are hired at the local level, and also by states," Romney said. "The federal government doesn't pay for teachers, firefighters or policemen. So obviously, that's completely absurd."

That triggered a new round of criticisms of Romney's understanding of federal aid to state and local governments.

Since then, Romney's "firemen" remarks and Obama's "private sector is doing fine" comment have been endlessly rehashed in campaign videos, news releases, cable TV, talk radio and elsewhere. They are virtually certain to live on in political ads in at least a dozen competitive states through Nov. 6.

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AP Economics Writer Christopher Rugaber contributed to this report.

Here is a playlist of Romney's 'Greatest Hits' from the campaign.
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  • With A Little Help From My Friends (Joe Cocker)

    <strong><a href="http://www.huffingtonpost.com/2012/05/28/mitt-romney-will-not-repu_n_1551540.html" target="_hplink">(May 28, 2012) --</a></strong> Despite a resurgence of <a href="http://www.thedailybeast.com/articles/2012/05/25/mitt-romney-s-new-bff-donald-trump.html" target="_hplink">Donald Trump's birther claims</a>, Romney refused to repudiate the billionaire, who has been helping with his 2012 campaign efforts. "You know, I don't agree with all the people who support me ... I need to get 50.1 percent or more and I'm appreciative to have the help of a lot of good people," Romney said. (Photo by Ethan Miller/Getty Images)

  • Who Let The Dogs Out (Baha Men)

    <strong><a href="http://www.huffingtonpost.com/2012/04/16/mitt-romney-seamus_n_1429925.html" target="_hplink">(April 16, 2012) -- </a></strong> In an interview with ABC's Diane Sawyer, Romney discussed the political fallout over strapping his dog Seamus to a car roof. He admits that he probably would not do it again. (Handout)

  • It's The End Of The World As We Know It (R.E.M.)

    <strong><a href="http://www.huffingtonpost.com/2012/04/04/mitt-romney-medicare-president-obama_n_1403267.html" target="_hplink">WASHINGTON, D.C. (April 4, 2012) --</a></strong> Speaking before the Newspaper Association of America, Romney attacked Barack Obama on his health record, claiming the president "has taken a series of steps that end Medicare as we know it." (Photo: Jim Watson/AFP/Getty Images)

  • For The Love Of Money (The O'Jays)

    <a href="http://www.huffingtonpost.com/2012/03/14/mitt-romney-i-made-a-lot-of-money_n_1345516.html" target="_hplink"><strong>NEW YORK, N.Y. (March 14, 2012) -- </strong></a> Romney became testy on Fox News while discussing his appeal to lower-income voters. On the same day, Occupy Wall Street protesters staged a demonstration outside Mitt's Waldorf Astoria hotel fundraiser. (Photo: Emmanuel Dunand/AFP/Getty Images)

  • People Are Strange (The Doors)

    <strong><a href="http://www.huffingtonpost.com/2012/03/09/mitt-romney-south_n_1334478.html" target="_hplink">PASCAGOULA, Miss. (March 9, 2012) --</a></strong> While on the trail in Alabama and Mississippi, Romney got in touch with his Southern side, learning how to say "y'all" and liking his grits. With those new experiences in hand, he admitted that "strange things are happening to me." (Photo: AP/Evan Vucci)

  • Pink Cadillac (Bruce Springsteen)

    <a href="http://www.huffingtonpost.com/2012/02/24/mitt-romney-cadillac_n_1299740.html" target="_hplink"><strong>DETROIT, Mich. (Feb. 24, 2012) -- </strong></a> While speaking before the Detroit Economic Club at Ford Field, Romney listed not two, not three, but four American-made cars that he and his wife, Ann, owned. Among the vehicles: "a couple of Cadillacs." (Photo: Scott Olson/Getty Images)

  • It's The Hard-Knock Life (Annie & The Orphans)

    <strong><a href="http://www.huffingtonpost.com/2012/02/01/mitt-romney-very-poor_n_1246557.html" target="_hplink">TAMPA, Fla. (Feb. 1, 2012) --</a></strong> In an interview with CNN, Romney noted that he is "not concerned about the very poor," citing the social safety net for that segment of the populace. (Photo: Ethan Miller/Getty Images)

  • America The Beautiful

    <a href="http://www.huffingtonpost.com/2012/01/31/mitt-romney-america-the-beautiful-_n_1243908.html" target="_hplink"><strong>THE VILLAGES, Fla. (Jan. 31, 2012) --</strong></a> On the eve of Florida's primary, Romney led his supporters in a singing of the patriotic song. (Photo: Emmanuel Dunand/AFP/Getty Images)

  • Successful (Drake, Lil Wayne)

    <a href="http://www.huffingtonpost.com/2012/01/19/mitt-romney-tax-returns_n_1217708.html" target="_hplink"> <strong>CHARLESTON, S.C. (Jan. 19, 2012) -- </strong></a> During CNN's GOP debate, Romney refused to commit to disclosing his tax returns, offering no apologies for his success. (Photo: Emmanuel Dunand/AFP/Getty Images)

  • Bye Bye Bye ('N Sync)

    <a href="http://www.huffingtonpost.com/2012/01/09/mitt-romney-i-like-being-able-to-fire-people_n_1194115.html" target="_hplink"><strong>NASHUA, N.H. (Jan. 9, 2012) -- </strong></a> In a speech about insurance options, Romney tells audience members, "I like being able to fire people who provide services to me." (Photo:AP/Charles Dharapak)

  • Don't Know Why (Norah Jones)

    <strong><a href="http://www.huffingtonpost.com/2011/10/28/mitt-romney-embraces-climate-change-denial_n_1063905.html" target="_hplink">PITTSBURGH, Pa. (Oct. 27, 2011) --</a></strong> Back in June 2011, Romney said humans are somewhat tied to climate change. By October, he had reversed course, saying "We don't know what causes climate change." (Photo: Jim Watson/AFP/Getty Images)