WASHINGTON -- The ingredients of a new immigration bill are beginning to take shape, with many Republicans now rushing to join Democrats to develop a comprehensive plan.

Republicans were stung by the recent elections, in which Latinos overwhelmingly supported President Barack Obama for another term. Conservative leaders and commentators immediately said the party had to become more welcoming to the nation’s fastest-growing voting bloc, and for many that meant reversing course on considering immigration policies that hard-liners previously had likened to amnesty.

Even conservative Fox News host Sean Hannity, reflecting on the Latino vote, told radio listeners that he’s “evolved” and now supports a pathway to citizenship. “We’ve got to get rid of the immigration issue altogether,” he said.

Obama, meanwhile, said this week that he’d make immigration one of his first legislative priorities. Criticized in the past for not putting forth specific legislative ideas, the president said his staff already had been in touch with Congress about what a plan might look like.

The key concepts – beefed-up border security and a pathway to legal residence for 11 million illegal immigrants – are similar to earlier proposals, which means that success probably will depend less on new ideas and more on the nation’s changing demographic and electoral realities.

The hurdles to an agreement are huge: The immigration debate in Washington has remained in a stalemate for much of the past decade. The last immigration-related law adopted was in 2005, and it required states to check the citizenship or legal-residence status of any applicants for driver’s licenses. There’s strong opposition within the Republican-led House of Representatives to a path to citizenship.

But this week both Democrats and Republicans on Capitol Hill spoke as if they finally could reach agreement on a solution to address the estimated 11 million people who are living in the country illegally.

There’s general consensus on stronger border protection, employment verification and a path to legal status for some illegal immigrants. What’s in dispute is what type of path to legal residence, for how many and whether it would include citizenship. Leaders also anticipate arguments over a bigger guest-worker program.

“Everything is broken,” Sen. Charles Schumer, D-N.Y., said in an interview. “We need to fix it all.”

Schumer and Sen. Lindsey Graham, R-S.C., who helped lead previous bipartisan efforts, already have begun talks. Others who are expected to participate include Sens. John McCain, R-Ariz., Richard Durbin, D-Ill., Robert Menendez, D-N.J., and Rand Paul, R-Ky., Graham said.

“We’ll be getting the band back together again,” said Graham, who along with McCain had been forced to abandon previous support of comprehensive overhaul efforts because of pushback from their constituents and national opposition.

Discussions reopened this month after Latino voters came out in force to help re-elect Obama. The president supported comprehensive restructuring and used his executive power this summer to prevent hundreds of thousands of undocumented youths who’d been brought to the country by their parents from being deported.

Republican presidential challenger Mitt Romney advocated during the primaries for hard-line polices that promoted “self-deportation,” and he tapped one of the authors of Arizona’s controversial immigration law as an adviser. Among other provisions, the law requires police to check the status of anyone they suspect is in the country illegally.