In a bold prediction that immediately agitated Republicans, Democratic Sen. Chuck Schumer claimed Sunday that the House ultimately will pass the Senate's comprehensive immigration bill -- despite House Speaker John Boehner's claims to the contrary. 

Schumer, needling the House speaker during an interview on "Fox News Sunday," claimed that Boehner will be pressured by the "dynamics" of the debate. 

"I believe that by the end of this year, the House will pass the Senate bill," Schumer said. 

Further, he claimed Boehner would have to rely largely on Democrats to pass it. This would constitute a violation of the so-called "Hastert rule" -- an unofficial policy named after former Speaker Dennis Hastert, under which the House only passes bills with a majority of the majority party on board. 

Violating that "rule" could damage Boehner's support inside the party, and Boehner has indicated he has no plans to do so. 

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Boehner said Thursday that "we're going to do our own bill" and it will reflect "the will of our majority." 

In reaction to Schumer, Boehner spokesman Michael Steel also told FoxNews.com that the speaker and his caucus have been "perfectly clear" on their intentions. 

"The House will not simply take up and pass the Senate bill," he said in an email. "Our legislation will reflect our principles, particularly on border security. Wishful thinking, frankly, is not a strategy for getting a bill to the president's desk." 

But Schumer, speaking after the Senate passed its version on Thursday, predicted several factors could change Boehner's mind. First, he said the coalition of both religious and business groups could pressure the House to act. Further, he said the national Republican leadership could do the same, citing the political importance of passing immigration legislation. 

Schumer, D-N.Y., also said supporters of the bill would be insistent. "We're not going to let this issue go away," he said. 

Rep. Trey Gowdy, R-S.C., also speaking on "Fox News Sunday," rejected Schumer's legislative prediction. 

"I was moved almost to the point of tears by Senator Schumer's concern for the future prospects of the Republican Party," Gowdy said, sarcastically. "But we're going to not take his advice." 

He added: "The Senate bill is not going to pass in the House. It's not going to pass for myriad reasons." 

He, like other House Republicans, questioned Senate promises that their bill would offer legalization to illegal immigrants in the near-term while eventually building border security and immigration enforcement for employers. 

The House is proceeding to break up the immigration issue into a series of piecemeal bills -- though Schumer claims they will not pass, leaving the House with the Senate bill as its only option. Gowdy noted that several House bills have already passed out of committee. "I'm more interested in getting it right than doing it on Sen. Schumer's schedule," he said. 

Sen. John McCain, R-Ariz., who also supports the bill, was more restrained when asked about what Boehner might do. 

"I respect and admire John Boehner," he said, adding it's not "appropriate" to tell him how to do his job.