A special meeting of the conference was called Monday during which leaders were expected to present a plan for discussion and could make a final decision based on how members respond, the Hill reported.
One contender is a reversal of the military pension cuts that were part of the bipartisan budget deal reached in December, a senior aide said.
The $17 trillion debt ceiling, held in abeyance as part of the December budget deal, went back into effect Friday. Treasury Secretary Jack Lew warned a possible default could occur Feb. 27 unless Congress acts.
After it adjourns Wednesday, the House won't be back in session until Feb. 25. To pass debt limit legislation this week, GOP leaders must post a bill online Monday to comply with chamber's three-day layover rules.
If Republicans can't find enough support for a plan during Monday's meeting, they might have to rely on Democratic votes by bringing a no-strings-attached bill that would raise the debt limit to the floor.
House Democrats have advocated passage of a bill that is free from strings. Beyond that, the Democratic-controlled Senate and President Obama also called for a bill focused solely on raising the debt ceiling.
The U.S. Chamber of Commerce, the nation's main business lobby, called on the House Monday to pass a "timely increase" to the debt ceiling, adding more pressure on Republicans, the Hill said.
The chamber's chief lobbyist, Bruce Josten, said in a letter that hiking the debt limit would erase the threat of default, allow credit markets to function properly and allow the economy to "achieve some long-awaited momentum."
Millions of Getty images now available for free via embed tool
Ray Liotta sues skin care company over use of likeness