House Republicans floated a three-part plan Tuesday to fund most of the government through the end of the fiscal year, temporarily fund the Homeland Security Department, and vote to symbolically rebuke President Obama for his executive order on immigration.

Speaker John Boehner told the GOP Conference in a closed-door meeting that the House will vote on an omnibus bill that would fund the government through September but fund DHS only through March. The plan, which had been floated theoretically for weeks, would give the House another opportunity to confront the president on immigration funding early next year.

At the same time, the House will vote on a separate bill from Rep. Ted Yoho of Florida stating that the president does not have the authority to shelter undocumented immigrants from deportation.

Boehner declined to announce the plan publicly at a press conference directly after the private meeting; rather, he noted that he is looking at "a variety of options, both for right now and when Republicans control both houses of the Congress next year."

"This is a serious breach of our Constitution," Boehner said, referring to Obama's immigration order. "It's a serious threat to our system of government. And frankly, we have limited options and limited ability to deal with it directly. But that's why we're continuing to talk to our members. We've not made decisions about how we're going to proceed, but we are, in fact, going to proceed."

Despite pressure from outside groups, such as Heritage Action, he noted that most of his members understand that blocking the president's order will be easier next year when Republicans also control the Senate.

It is unclear whether the plan being discussed has support from enough members in the conference. Some members at the meeting raised the idea of also temporarily funding other agencies involved in immigration, such as the Justice Department. Boehner's strategy would need strong GOP support, because House Minority Leader Nancy Pelosi has said she and her fellow Democrats would only support a "clean" omnibus that funds the whole government.

Senate Democrats, who will keep control of that chamber for another month, are also opposed to a plan that doesn't fully fund Homeland Security. And the Obama administration likewise dislikes the idea. Homeland Security Secretary Jeh Johnson testified at a House hearing Tuesday morning that temporary funding would make it harder to run his department effectively.

Rep. Bennie Thompson, D-Miss., ranking member of the House Homeland Security Committee where Johnson testified, said the emerging plan would hurt DHS operationally.

“Singling out DHS, by funding it through a continuing resolution, undermines its ability to carry out its critical homeland security mission such as protecting our air, land and sea borders and cyberspace,” Thompson said. “It also unfairly punishes state and local governments and first responders who rely on federal grants for emergency management and terrorism prevention activities.”

Rep. Dennis Ross, a member of the GOP whip team, said Republicans had "learned from what happened last time" the party had a spending showdown with Obama, and they want to avoid another government shutdown.

Ross was skeptical that his party's plan would attract Democratic votes but expressed confidence most Republicans would unite behind it. Party conservatives, Ross said, "want to vote for it, but they're wrestling with what the details are going to be."

Yet within an hour after leaders floated the plan, some members began to push back. At a periodic roundtable of conservative-minded members, several Congressmen said they would rather vote for a short-term continuing resolution that would fund the entire government through January or February.

"The voters understand that the cavalry is coming," Rep. Jim Jordan said. "Why in the world would you want to extend a CR, a funding bill, for several months out? Why not wait for those people to get here?"

Rep. Mo Brooks of Alabama also said there was still considerable disagreement over how the GOP should move forward.

Before the meeting with Boehner, some of the GOP's border hawks gathered to formulate their own options. Brooks said there was enough dissent to "influence the outcome of what the House does." Brooks said he was not "optimistic" that Boehner was going to move on a strong enough plan to satisfy the conservative members of the conference.

Yoho, meanwhile, told reporters Tuesday that his bill to express dissatisfaction with the president could be more than a "symbolic" message if the Senate took it up, though that is exceedingly unlikely.

Yoho says he approached leadership before Thanksgiving last week to seek their support. While Yoho is not a natural ally for leadership and is typically seen as part of the "hell no" caucus, leaders were open to this bill, as it might assuage some more-conservative members who wanted to wage an immediate funding fight.

"My hat's off to the leadership," Yoho said. "I commend leadership for saying, 'You know what, this sounds like a commonsense bill.' "

Asked as they were leaving their Tuesday morning press conference if a shutdown was on or off the table, House Republican leaders chuckled and exited the room without answering.

Rachel Roubein and Eric Katz contributed to this article.