House Republicans could demand a pre-conference agreement guaranteeing the parameters of any immigration-reform compromise with the Senate as the price for green-lighting a conference committee to negotiate a final bill.

Whether House Republicans should even consider a conference committee with the Senate to hash out differences on comprehensive immigration reform will likely be discussed Wednesday, during a private meeting the House GOP scheduled to discuss the matter. Some opponents of the Senate-passed bill, which House Speaker John Boehner, R-Ohio, has already declared dead in the lower chamber, are urging House Republicans to shun a conference committee altogether.

Rather than a comprehensive approach, House Republicans are moving a handful of immigration bills that are narrowly focused on specific issues - like border security and expanding legal immigration - and broadly supported by the GOP majority. But even some House Republicans who favor bipartisan immigration reform are concerned that the Senate conferees could collude with House Democrats on the conference committee to craft a compromise that looks more like the Senate package and ignores House GOP priorities.

"I think our conference, in order to move forward, has to feel that there's not going to be any kind of gaming," said Rep. Raul Labrador, R-Idaho, who until recently was a member of the bipartisan House group that is negotiating comprehensive immigration reform.

Moving to assure the outcome of a House-Senate conference committee would add yet another political complication to the increasingly difficult effort to move a comprehensive immigration reform bill through the Congress.

Congressional Republicans were already suspicious that President Obama might skirt the border security mandates in the Senate package, which most believe is too weak on enforcement to begin with, particularly because it would immediately legalize millions of illegal immigrants and offer them a path to citizenship.

But the administration's decision last week to delay the implementation of key components of Obama's health care reforms - the president's signature legislative achievement - have only stoked the concerns of House Republicans. They fear that Obama would find a justification to ignore the tougher border security measures they are sure to demand in exchange for allowing a final package that includes legalization and citizenship to receive floor vote.

Boehner has not yet committed to a pre-conference agreement - at least publicly - and not all Republicans are convinced he would back it. But anxiety among Republicans that House Democrats on the conference committee might vote as a bloc with a unified team of Senate conferees, and hijack the negotiations, is real. Consequently, Boehner is unlikely to approve a conference committee that isn't governed by some sort of agreement that protects House Republicans.

"I would anticipate that we're going to have some red lines that we can't cross, going into the conference," said House Homeland Security Chairman Michael McCaul, R-Texas, whose committee is responsible for processing some of the bills that would shape the House's version of immigration reform legislation.

Pre-conference agreements are relatively common. House Budget Chairman Paul Ryan, R-Wis., has been trying to reach an accord with Senate Budget Chairman Patty Murray, D-Wash., before agreeing to proceed to a conference committee to reconcile the chambers' competing 2014 budget plans. Ryan said he's concerned that an unwieldy conference committee could inflame partisan tensions; Democrats accuse him of wanting to hide his budget plan from the public.

Meanwhile, House rules allow the minority caucus to force floor votes on almost any subject once a conference committee runs longer than 10 legislative days, or 20 calendar days, depending on which threshold is reached first. That could be a consideration for Boehner as he gauges his options for a conference committee, as negotiating a comprehensive immigration bill could take several weeks.

Of course, House Republicans have the votes to kill any immigration reform bill approved by a conference committee. But even staunch opponents of immigration reform concede that allowing the process to get that far along could produce a scenario that is unpredictable and politically problematic. As it stands now, there's minimal public pressure on the House to move an immigration bill.

"I think we would have a real strong line in the sand, that we don't want to pass anything that would open the door to an uncontrolled conference," Rep. Jack Kingston, R-Ga., said. " think we would because people, a lot of times will vote for a bill, with the cover of, I'll vote against the conference, but I think in this one we are very concerned about the policy."