Not even they know.
Some have proposed major changes to workplace coverage, even turning Medicare into a voucher plan. Many prefer small steps that tiptoe around political land mines. Others want a clean start.
"During the health care debate there was just as much division within Republicans as there was between the parties," said Douglas Holtz-Eakin, a leading adviser to 2008 GOP presidential candidate John McCain.
One of the first acts of a Republican majority would be a vote to repeal what they dismiss as "Obamacare." But they haven't said much about what would replace it.
A GOP bill rejected by the Democratic-led House last year is the closest thing to a starting point.
The Republican plan would cover an additional 3 million people by 2019, compared with nearly 33 million under the Obama health care law. It would lower premiums modestly for many small businesses and for people buying insurance directly. It wouldn't solve the nation's long-term cost and coverage problems.
"On a scale of 1 to 1,000, it's about a 5," scoffs former Senate Majority Leader Tom Daschle, a senior Democratic adviser.
Yet some Republican proposals are as far-reaching as anything Democrats have tried. A budget crisis could push them to the forefront because lowering health costs is critical to reducing record federal deficits.
Many of those ideas come from Rep. Paul Ryan, R-Wis., one of a group of younger lawmakers trying to energize the party leadership.
Along with Sen. Tom Coburn, R-Okla., Ryan sponsored legislation that would begin to wean the middle-class away from job-based coverage and replace Medicaid with private insurance for most low-income people.
Their plan would make employer coverage taxable to the employee, but that would be offset with a tax credit. It could be used to buy coverage individually or to keep a plan at work. Some people with generous employer coverage could face higher taxes under the Republicans.