WASHINGTON — House Republicans, increasingly isolated from even some of their strongest supporters more than a week into a government shutdown, began on Wednesday to consider a path out of the fiscal impasse that would raise the debt ceiling for a few weeks as they press for a broader deficit reduction deal.

That approach could possibly set aside the fight over the new health care law, which prompted the shutdown and which some Republicans will be reluctant to abandon.

In a meeting with the most ardent House conservatives, Representative Paul D. Ryan of Wisconsin, the chairman of the House Budget Committee, laid out a package focused on an overhaul of Medicare and a path toward a comprehensive simplification of the tax code.

“We’re more in the ideas stage right now,” said Representative Jack Kingston, Republican of Georgia and a senior member of the Appropriations Committee. “There is a developing consensus that this is a lot bigger than an Obamacare discussion.”