* Appeal to be aimed at Hispanic voters, who favor Obama
* Romney looking to rebound after a tough week
By Steve Holland
LOS ANGELES, Sept 17 (Reuters) - Republican presidential candidate Mitt Romney will pledge to Hispanics on Monday that if elected he will fix the troubled U.S. immigration system in an appeal to a rising voter bloc that overwhelmingly favors Democratic President Barack Obama.
Looking to rebound after a tough week in which he fell behind Obama in the polls, Romney will couple his immigration promises with a commitment to get a handle on America's problem of rising national debt and massive budget deficits.
This is part of the Republican's drive to spend more time talking about the specifics of his economic proposals in answer to voter demands for more information as they choose between him and Obama in the Nov. 6 election.
Romney's immigration remarks to the Hispanic Chamber of Commerce will be aimed at shoring up a weakness in his candidacy: the fact that a huge majority of Hispanics support Obama.
"Americans may disagree about how to fix our immigration system, but I think we can all agree that it is broken," Romney will say.
In excerpts of his speech released by his campaign, Romney did not get into the specifics of how he would patch up a deep divide between Democrats and Republicans on the approach to repairing the U.S. immigration system.
The last serious attempt at an immigration overhaul, made by Republican President George W. Bush in 2007, collapsed in Congress as conservatives rebelled against the plan, which they called an amnesty for the estimated 12 million illegal immigrants already living in the United States.
After promising during his 2008 campaign to take on the immigration issue, Obama never followed through, leading to disappointment among various Hispanic groups.
Romney will point to Obama's inability to work on the problem as a failure.
"Candidate Obama said that one of his highest priorities would be to fix immigration in his first year in office. Despite his party having majorities in both houses of Congress, the president never even offered up a bill," Romney will say.
U.S. BORDER INTEGRITY
Romney will vow to "work with Republicans and Democrats to permanently fix our immigration system," while stressing that any plan must first ensure the integrity of U.S. borders - a problem on which the Obama administration says it has already made progress.
"I believe we can all agree that what we need are fair and enforceable immigration laws that will stem the flow of illegal immigration, while strengthening legal immigration," Romney will say.
The Republican's campaign is built around pledges to improve the U.S. economy and spur job growth and he has used the same message in appealing to Hispanics with the view that all Americans want a good job whatever their ethnicity.
"While national unemployment is 8.1 percent, Hispanic unemployment is over 10 percent. Over two million more Hispanics are living in poverty today than the day President Obama took office," Romney will say.
His campaign is trying to recover from a week in which Romney made a political issue of the deaths of four Americans in Libya, prompting criticism from Democrats and some Republicans that he had botched his reaction to a national tragedy.
Obama also has enjoyed a bounce in support from the Democratic National Convention in late August, forcing Romney to play catch-up in a race that appeared to be turning against him.
A Gallup poll on Sunday, however, suggested Obama's bounce was dissipating with his lead reduced to 3 percentage points - 48 percent to 45 percent for Romney.
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33 out of 100 seats are up for election. 51 are needed for a majority.
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* Includes two independent senators expected to caucus with the Democrats: Angus King (Maine) and Sen. Bernie Sanders (Vt.).
All 435 seats are up for election. 218 are needed for a majority.