CAMBRIDGE, Md. >> House Republicans on Friday agreed they should “go big” in 2014, with a real legislative agenda to bring to voters in November.

“How else do you project a bold alternative option for the country?” asked Rep. Jim Jordan of Ohio, an influential conservative.

But a three-day issues conference ended here Friday with Republicans divided over which initiatives to embrace and which to jettison, and there were no concrete decisions on the most pressing issues facing the lawmakers: how to raise the borrowing limit ahead of a potential debt default by the end of February; an overhaul of immigration laws; a legislative alternative to the Affordable Care Act; and whether to press forward with a rewrite of the tax code.

Rep. Eric Cantor of Virginia, the House majority leader, did promise a vote on a health care alternative this year, the closest thing to a decision. But House members say he left it unclear whether the vote would be on a full-scale replacement for the health care law, or a less comprehensive measure.

In a lengthy, closed-door discussion of the debt limit Friday morning, members failed to unite around concessions they would seek from President Barack Obama in exchange for raising the government’s borrowing limit, but even some of the House’s most ardent conservatives signaled they were ready to scale back expectations to avoid another budget showdown.

Many members focused on linking the debt ceiling to repealing a provision of the president’s health care law that would provide federal assistance to insurance companies if the people who sign up for their plans through the law are too weighted to the sicker and the older. The provision was designed to avoid sharp rate increases next year if not enough younger, healthier people purchase insurance through the health exchanges.

Rep. Paul Ryan of Wisconsin, the chairman of the House Budget Committee, embraced the plan. At one point, according to senior aides in the room, Rep. Kevin McCarthy of California, the No. 3 Republican in the House, asked Rep. Michele Bachmann of Minnesota, a longtime opponent of any debt-ceiling increase, if she would vote to lift the debt limit with that “no bailout” provision attached.

She said yes, according to the aides.

But other ideas were pushed as well. They included attaching approval of the Keystone XL oil pipeline to a vote to raise the debt limit; making changes in the budget process, including moving to two-year budgets; and changing the definition of a part-time worker under the health care law. Currently a part-time worker is defined as someone who works fewer than 30 hours a week. A suggestion to change that definition to someone who works fewer than 40 hours a week has bipartisan support, with members of both parties worried that employers are cutting workers’ hours to avoid having to offer them insurance under the law’s requirements.

But there was no consensus. Some Republicans worry that adjusting the work-hour definition would be seen as fixing the health care law rather than repealing it.

There was broad acceptance, however, that the debt ceiling did have to be raised, a change of position for many Republicans who, since 2011, have maintained that freezing the debt limit would not bring the economic disaster most economists foresee. Doug Holtz-Eakin, a Republican economist and a former Congressional Budget Office director, opened the session with an explanation of why Congress must raise the borrowing threshold.

If Republicans want to extract even minor concessions, they will have to move soon, within the next seven to 10 days, aides said. But no deadline was set.

Democrats, led by Treasury Secretary Jacob J. Lew, have held firm that they will not accept any concessions attached to a debt-limit increase.

“The more time Republicans spend dreaming up their latest debt limit wish list, the closer they are pushing workers and the economy toward another completely unnecessary crisis,” said Sen. Patty Murray, D-Wash. “The American people are sick and tired of Republicans playing games with our economic recovery, and Democrats have made it clear that Republicans don’t get to demand a ransom simply for allowing Congress to do its job.”

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