A broad majority of Americans believe the government should allow undocumented immigrants to legally remain in the United States, according to a Pew Research Center poll released Thursday.

Strikingly, the poll found that majorities of Democrats, Independents, and even Republicans all favored that position, giving proponents of immigration reform reason to feel good about the odds of Congress agreeing to some sort of reform bill this year.

In the poll, 71 percent of respondents said there should be a way for the nation's estimated 11 million undocumented immigrants to legally remain in the U.S., while 27 percent said those immigrants should not be permitted to stay. Among those who favored granting legal status, a 43 percent plurality said those immigrants should be permitted to apply for full citizenship, versus 24 percent who said they should only be given permanent legal residency.

Sixty-four percent of Republicans agreed that illegal immigrants should be allowed to legally remain in America, nearly double the 34 percent who said otherwise.

Republicans' views are particularly notable, since it indicates the party has indeed begun to move away from its once-strident opposition to immigration reform. Republicans scuttled President George W. Bush's reform efforts during his presidency, and just three years ago, Sen. John McCain (R-Ariz.) reversed his longstanding support for reform when faced with a primary challenge, calling instead for Washington to defend the border and "complete the danged fence." (In recent months, McCain has flipped back to his earlier persona as a reformer.)

Since then, however, the party has acknowledged its problem with Latino voters and made courting that demographic a cornerstone of its big rebranding effort. At the same time, high-profile Republican politicians, including former Florida Governor Jeb Bush and Sen. Marco Rubio (R-Fla.), are pushing the party to embrace immigration reform in one shape or another, with conservative strategist Dick Morris warning that a failure to do so would see the GOP "exiled to being a footnote in history."

Pew's results back up the findings of other recent polls that have found strong support for immigration reform. A Public Religion Research Institute and Brookings Institution survey released last week found that 63 percent of all Americans — including a majority of Republicans — supported a so-called "pathway to citizenship" for undocumented workers. A recent Bloomberg poll that used different phrasing found that a slightly smaller 53 percent majority of Americans supported a citizenship path.