Conservative Republicans are pushing back hard against House Speaker John Boehner's plan to effectively push off the battle over President Obama's immigration plan to next year in order to pass a spending bill, increasing the likelihood he'll need help from Democrats to get it through the House and Senate. 

The speaker on Tuesday had put forward a plan to address two tricky issues: letting Republicans vent over the president's controversial immigration executive actions, while also backing a spending bill to keep the government running past Dec. 11, when current funding runs out. 

Boehner's solution is to call a vote on a bill this week opposing and trying to block Obama's immigration orders -- though it would likely die in the Senate. Then, the House would vote next week on a bill funding the government through the full fiscal year, and funding immigration-related agencies through early next year. This would kick the fight over the president's immigration plan to 2015, when Republicans have control of both chambers. 

But that's not enough for many conservatives, who want to use the current spending fight as leverage to defund the president's plan now. They complain that the planned vote this week would merely be symbolic. 

Sen. Jeff Sessions, R-Ala., blasted Boehner's proposal in a statement late Tuesday, suggesting it violates a campaign promise by Republicans to do "everything" they can to stop executive "amnesty." 

"Unfortunately, the plan now being circulated in the House fails to meet that test," Sessions said. 

Sen. David Vitter, R-La., said "sending a bill to the Senate without first making an attempt to include defund language is telling the American people that you support Obama's executive amnesty. That would be a slap in the face to the voters who sent a message last month by electing Republican majorities in Congress." 

Sen. Ted Cruz, R-Texas, on Wednesday urged GOP colleagues to "do what you said you would do" to battle the "amnesty." 

Boehner is likewise facing some pushback from conservative members of the House GOP caucus. This increases the likelihood that he'll need help from Minority Leader Nancy Pelosi and her Democratic rank-and-file. 

Such an alliance would not be unprecedented. Boehner routinely has turned to Democrats to pass major pieces of legislation when he couldn't bring his full caucus on board, including to avert a partial government shutdown. As it stands now, Republicans can only lose 18 of their own before having to turn to Democrats to prevent a partial shutdown.

Pelosi has not definitively said what she might do with the current package. 

And on the Senate side, Democratic Leader Harry Reid on Tuesday would not rule out accepting the House GOP spending proposal, though Democrats would rather see a spending bill that funds the government in its entirety through the end of the fiscal year. 

Reid called the Republican effort to only fund the Department of Homeland Security through March "a shame." But the Nevada Democrat didn't completely torch the House Republican maneuver. 

Republican sources indicated there may be some "softness" in GOP ranks for the Boehner plan, but GOP aides noted that over the past four years, the Republican Conference has traditionally lost 30-50 members on its side when it comes to voting on big legislative initiatives. "This is just what we always go through," lamented one senior aide familiar with previous vote-counting efforts. 

Boehner and his allies are touting the working plan as the best course of action, with the understanding that they would resume the fight next year over Obama's plan to grant temporary legal status to up to 5 million illegal immigrants. 

Boehner said Tuesday that Obama has ignored the American people. 

"This is a serious breach of our Constitution," Boehner said. 

He also said lawmakers "have limited options and abilities to deal with it directly." 

Fox News' Chad Pergram contributed to this report.