Senate Republicans’ decision to largely line up against the confirmation of Sonia Sotomayor to the Supreme Court has been bolstered by their success at cutting into President Barack Obama’s public support and building opposition to the Democratic agenda.

Only a handful of Republicans have said they will end up supporting Sotomayor, and virtually all of them have been harshly criticized by the party’s conservative wing as a result.

Even GOP Judiciary Committee members Orrin Hatch (Utah) and Chuck Grassley (Iowa), who in their tenures have backed every other Supreme Court nominee, have come out against the nomination. Republicans argue that the brightening political landscape for the minority is at least partially responsible.

“Absolutely. If Republicans were not making inroads with independents on virtually every other issue, this would be a much more perilous vote,— a senior Republican leadership aide said.

“The burden of proof would lie with Republicans to show why people should ever vote for Republicans again,— the aide added.

Earlier this year, a number of high-profile Republicans, including Conference Chairman Lamar Alexander (Tenn.) — who last week announced he is voting for Sotomayor — argued that the party needs to find ways to broaden its appeal beyond its conservative base. Others, including Sen. George Voinovich (Ohio), have repeatedly criticized the party for supporting an agenda heavily tilted toward a Southern, Christian, white GOP base.

Republican leaders have been struggling to rebuild their relationship with the Hispanic community, which was damaged after the party’s mishandling of immigration reform in 2005-06.

At the same time, Republican Members have come under increasing pressure from the party’s base to stay true. Grassley, for instance, has taken heat from Republicans in Iowa over the past two years for his willingness to work with Democrats on fiscal matters.

But a string of recent polls show that Obama’s popularity has taken a hit over the past several months over issues such as the economy, the closure of the Guantánamo Bay, Cuba, prison and health care reform.

A recent poll conducted by Greenberg Quinlan Rosner Research and Public Opinions Strategies showed that in a generic matchup, 43 percent of respondents favored Republicans while 42 percent chose Democrats.

“In every poll, it shows the constituency has flipped — that is, independents, self-proclaimed independents, have shifted,— one Republican said.

With the Sotomayor confirmation coinciding with Obama’s slipping public approval, many Senate Republicans say they are finding the political landscape much less treacherous than had first been thought. That, they argue, is making it easier for Members to stick close to the party’s base on the nomination.

So far, just six Republicans have said they will support Sotomayor this week: Sens. Lindsey Graham (S.C.), Dick Lugar (Ind.), Mel Martinez (Fla.), Alexander, and Olympia Snowe and Susan Collins of Maine.

Republicans also haven’t seen the kind of backlash that many feared would come from broad opposition to the first Latina nominee to the Supreme Court, in part because they took steps to avoid an bitter confirmation hearing. Opposition to Republicans “didn’t present itself because Republicans handled themselves in a dignified way— throughout the hearings, the leadership aide said, noting that Members repeatedly sought to limit their criticism to her judicial philosophy and steered clear of getting personal.

Nevertheless, Republican moderates warned that the party could still experience aftershock from the Sotomayor vote.

Graham, who was the only Judiciary Republican to vote for Sotomayor, argued that the immigration debacle in particular hurt the GOP and that the confirmation process provides a chance to heal some of those wounds. “We lost a lot of ground with Hispanics because certain elements of the party’s rhetoric was so harsh. The party label was hurt by that … [and] we’ve got a chance to rebuild that.—

Graham also rejected some conservatives’ charges that supporting Sotomayor is a repudiation of the party’s roots. “I’m very conservative … socially and fiscally conservative. But I will break when I think it’s in the best interests of the party.—

Lugar, the longest-serving GOP Senator, said that while he did not “want to cast aspersions on [Senators’] reasons for voting,— for him it was a simple question of Sotomayor’s qualifications. “I think she’s a very fine jurist. The president of the United States should really have some respect in making these nominations, certainly for a talented, well-qualified nominee.—