What long has been a nonstarter for Republicans — raising tax rates on wealthy Americans — is now backed by GOP House Speaker John Boehner in his negotiations with President Barack Obama to avert a potential fiscal crisis. Party luminaries, including Louisiana Gov. Bobby Jindal, have started calling for a wholesale shift in the GOP's approach to immigration after Hispanic voters shunned Republican candidates. And some Republicans who previously championed gun rights now are opening the door to restrictions following a schoolhouse shooting spree earlier this month.

"Put guns on the table. Also, put video games on the table. Put mental health on the table," Rep. Jack Kingston, R-Ga., said last week. Other prominent Republicans echoed him in calling for a sweeping review of how to prevent tragedies like the Newtown, Conn., school shooting. Among those open to a re-evaluation of the nation's gun policies were Sens. Marco Rubio, R-Fla., and Chuck Grassley, R-Iowa.

"You've got to take all these things into consideration," Grassley said.

And yet, the head of the National Rifle Association, silent for a week after the Newtown shootings, has proposed staffing schools with armed police, making clear the NRA, which tends to support the GOP, will continue pushing for fewer gun restrictions, not more.

Meanwhile, Boehner's attempt to get his own members on board with a deficit-reduction plan that would raise taxes on incomes of more than $1 million failed last week, exposing the reluctance of many in the Republican caucus to entertain more moderate fiscal positions.

With Republican leaders being pulled at once to the left and to the right, it's too soon to know whether the party that emerges from this identity crisis will be more or less conservative than the one that was once so confident about the 2012 elections. After all, less than two months have passed since the crushing defeat of GOP presidential nominee Mitt Romney, who moved far to the right during the primary season and, some in the party say, lost the general election as a result.

But what's increasingly clear is that the party is now engaged in an uncomfortable and very public fight over whether its tenets, still firmly held within the party's most devout ranks, conflict with the views of Americans as a whole.

Many Republicans recognize that to remain relevant with voters whose views are changing, they too must change.

"We lost the election because we were out of touch with the American people," said John Weaver, a senior adviser to past presidential candidates John McCain, the GOP nominee in 2008, and Jon Huntsman, who sought the nomination this year.

The polling suggests as much.

While Republican candidates for years have adamantly opposed tax increases on anyone, an Associated Press-GfK poll earlier this month found roughly half of all Americans supported allowing George W. Bush-era tax cuts to expire on those earning more than $250,000 a year.

Most GOP candidates — Romney among them — also long have opposed allowing people in the country illegally to get an eventual path to citizenship. But exit polls from the Nov. 6 election showed most voters favored allowing people working in the U.S. illegally to stay.

And gun control has for decades been anathema to Republicans. But a Washington Post/ABC News poll published last week, following the Connecticut shooting, showed 54 percent of Americans now favor stronger restrictions.

This is the backdrop as Republicans undergo a period of soul-searching after this fall's electoral shellacking. Romney became the fifth GOP nominee in six elections to lose the national popular vote to the Democratic candidate. Republicans also shed seats in their House majority and lost ground to majority Democrats in the Senate.

Of particular concern is the margin of loss among Hispanics, a group Obama won by about 70 percent to 30 percent.

It took only hours after the loss for national GOP leaders to blame Romney for shifting to the right on immigration — and signal that the party must change.

Jindal, a prospective 2016 presidential contender, was among the Republicans calling for a more measured approach by the GOP. And even previously hard-line opponents of immigration reform — like conservative talk show host Sean Hannity — said the party needs to get over its immigration stance, which heavily favors border security over other measures.

"What you have is agreement that we as a party need to spend a lot of time and effort on the Latino vote," veteran Republican strategist Charlie Black said.

When Congress returned to Washington after the election to start a debate over taxes and spending, a number of prominent Republicans, including Sen. Tom Coburn of Oklahoma, the top Republican on the Senate Finance Committee, signaled they would be willing to abandon their pledges against raising taxes — as long as other conditions were met — as part of a package of proposals to avoid a catastrophic budget meltdown.

Leading the effort was Boehner, who has told Obama he would allow taxes to be increased on the wealthiest Americans, as well as on capital gains, estates and dividends, as part of a deal including spending cuts and provisions to slow the growth of entitlement programs. Obama, meanwhile, also has made concessions in the talks to avoid the so-called "fiscal cliff" by agreeing to a higher-income threshold for tax rate increases, while insisting that Congress grant him the authority to raise the debt ceiling. Both sides have spent the past several weeks bickering over the terms.

While some Democrats quickly called for more stringent gun laws, most Republicans initially were silent. And their virtual absence from the debate suggested that some Republicans who champion gun rights at least may have been reconsidering their stances against firearms restrictions.

By the Monday after the Connecticut shooting, MSNBC talk show host Joe Scarborough, a former Republican congressman from Florida, called for reinstating the ban on assault-style weapons, which he had opposed. The ban expired in 2004, despite support for it from Republican President George W. Bush. Referring to the shooting, Scarborough said: "I knew that day that the ideologies of my past career were no longer relevant to the future that I want, that I demand, for my children."

The next day, Grassley and Kingston were among the Republicans saying they were at least willing to discuss stronger gun laws.

"The party is at a point where it wants to have those discussions in public, where people feel comfortable differing from what is perceived as the party orthodoxy," said Republican consultant Dan Hazelwood.

If silence is a signal, shifts on other issues could be coming, chief among them gay marriage, which the GOP base long has opposed. Exit polls found half of all Americans say same-sex marriage should be legally recognized.

After three states — Washington, Maryland and Maine — voted last month to legalize gay marriage, the Republican leadership generally has remained quiet on the issue. There also has been no effort in the House or Senate to push major legislation, only narrower proposals, such as a move in the Armed Services Committee to bar gay marriages at military facilities.

But in a sign that the fight over gay marriage also may be waning within the GOP base, former House Speaker Newt Gingrich said it was time for Republicans to accept shifting public opinion.

The former Georgia congressman, who oversaw passage of the Defense of Marriage Act in Congress and helped finance state campaigns to fight gay marriage in 2010, said in a Huffington Post interview that the party should work toward acceptance of rights for gay couples, while still distinguishing them from marriage.

"The momentum is clearly now in the direction in finding some way to . accommodate and deal with reality," Gingrich said.