FUTURE IMPLICATIONS

Boehner has said an immigration bill will be put to a vote only if a majority of House Republicans back it. Boehner supports a piecemeal approach using smaller, targeted bills rather than the sweeping Senate legislation.

Republican Senator John McCain of Arizona, another member of the bipartisan group behind the Senate bill, said it would not be easy to convince the House to pass broad immigration reform but held out hope.

"I really hesitate to tell Speaker Boehner exactly how he should do this. But I think Republicans realize the implications (for) the future of the Republican Party in America if we don't get this issue behind us," McCain said on "Fox News Sunday."

"I believe that the coalition that we've assembled of support ranging from evangelicals, to the Catholic church, business, labor, farm workers, growers ... I frankly have never seen such widespread support. And I am hopeful that we can convince our House colleagues," McCain said.

Representative Nancy Pelosi of California, the top Democrat in the House, said she was optimistic the political realities of immigration would force House Republicans to come around.

"It's certainly right for the Republicans if they ever want to win a presidential race," Pelosi said on NBC's "Meet the Press" program.

A proposal being talked about in the House as an alternative to the Senate bill would offer possible citizenship in the future after illegal immigrants spend a decade working through a legalized status that gives them work permits.

Representative Robert Goodlatte of Virginia, chairman of the House Judiciary Committee, said it was possible the House could pass a measure that did not include a pathway to citizenship but focused on a "pathway to legalization" for undocumented immigrants. On ABC's "This Week" program, Goodlatte also made clear the House would not pass the Senate bill.

"When you use the word pathway to 'legalization' as opposed to pathway to 'citizenship,' I'd say, 'Yes,'" he said when asked about the chances for an immigration bill getting through the House.

"Not a special pathway to citizenship where people who are here unlawfully get something that people who have worked for decades to immigrate lawfully do not have," Goodlatte added.