WASHINGTON -- Mitt Romney is stuck between a fiscal cliff and a hard-right place.

On one side are unwavering conservatives who want their presumptive presidential nominee to hold the line on not raising federal revenues and a rigid pledge against supporting new taxes. On the other side are a growing number of Republican voices pleading with him to embrace revenue increases as a way to avoid the so-called fiscal cliff -- more than $100 billion in automatic spending cuts slated for early January.

After a news conference Thursday, retiring Rep. Steve LaTourette (R-Ohio) urged Romney's team "to make sure they read and understand Simpson-Bowles," referring to the failed bipartisan budget plan that would have combined taxes and spending cuts to trim the federal deficit by $4 trillion over the next decade.

"[Romney should] either get on board or say, 'Hey, I'm 90 percent there. I've got these three things.' And we'll work and fix the three things, if they're reasonable," LaTourette told reporters. "But to be silent and pretend it doesn't exist and be involved in all these sideshow issues -- that's not what people are interested in hearing."

LaTourette also decried House Republicans' ideological rigidity, citing it as one of the reasons he will not be seeking his 10th term in Congress. That same inflexibility permeates the fiscal cliff debate, he said.

"It's going to take Gov. Romney and President Obama to link hands and jump off this cliff together and understand that we got into this mess together and we're going to have to get out of this mess together," LaTourette said. "Republicans are going to have to start talking about revenues."

LaTourette's comments came a day after Sen. Lindsey Graham (R-S.C.) told reporters that Romney should welcome new revenues in any legislative effort to avoid the fiscal cliff.

"If he gave his blessing, it would be easier for Republicans," Graham said Wednesday, according to Politico.

In recent weeks, Graham has argued that Republicans need to talk about incorporating revenue hikes in the fiscal equation, at least in terms of closing tax loopholes.

He was less pointed in his sequestration advice on Thursday, including the White House as well. "Leadership from Romney and Obama would help," Graham told The Huffington Post.

At least one conservative, independent-minded Democrat wants to hear from the presumptive GOP nominee, too.

"I'm calling on a presidential candidate, Mitt Romney, to really put it all on the table," said Rep. Daniel Lipinski (D-Ill.) at the news conference with LaTourette and two other moderate Republicans. "Address the American people and say, 'This is a serious crisis we are facing.'"

The remarks from Graham and LaTourette constitute a noted departure from a GOP line of attack that has been aimed solely at Barack Obama: The White House, the attack goes, is failing to lead Congress toward a bipartisan solution. Dragging Romney's name into the partisan rancor amps up pressure on the GOP standard-bearer to articulate his own guidance.

The Romney campaign has made it clear that it will not let Obama off the hot seat over the Pentagon spending reductions that make up half of sequestration, the formal term for the upcoming massive budget cuts resulting from the failure of the congressional super committee to reach a deal last fall. "This is an important issue that doesn't go away until the devastating across-the-board cuts are addressed," Romney spokeswoman Amanda Henneberg told The Huffington Post on Tuesday. A Romney spokesman did not respond to several requests for comment Thursday.

Embracing revenue increases would require serious political maneuvering for Romney, who has signed the Taxpayer Protection Pledge, the anti-tax oath pushed by Americans for Tax Reform founder Grover Norquist.

In a news release and subsequent radio ad, the Romney campaign boasted about currying Norquist's favor in December 2006, when Romney signed the pledge after snubbing it during his 2002 run for Massachusetts governor. Then-deputy campaign manager Eric Fehrnstrom had told the Boston Globe that the pledge was "government by gimmickry."

Fact-checking website Politifact has already rated Romney's changing position on the Norquist pact as a full flip-flop.

On a conference call Thursday, Rep. Randy Forbes (R-Va.) said it's "fine" to put everything on the table in devising a legislative answer to the fiscal cliff. However, Romney has already made his views known, said Forbes, who chairs the readiness subcommittee of the House Armed Services Committee.

"I think Governor Romney has offered the most important guidance he can offer, which is he said one of the first things he would do when he's in office is to stop these massive, arbitrary cuts from taking place," Forbes said.

In a speech at the Veterans of Foreign Wars convention last month, Romney declared he "will not allow" the defense sequester to go into effect if he is elected president. But he did not outline any specific plan to derail it.

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