No. 2 Senate GOP leader John Cornyn of Texas said writing a new health care law would be a top priority in his chamber but stopped short of saying senators would complete that this year.
GOP Ohio Gov. John Kasich, whose state is covering hundreds of thousands of additional people under the health care law's Medicaid expansion, expressed concerns to reporters in Cleveland about whether Congress would follow repeal with a replacement.
The law created marketplaces where consumers can buy coverage and provided subsidies to help people afford premiums, expanded Medicaid for lower-earning people and set requirements for the types of care that insurers must cover.
Since the new Congress convened this week, Republicans have taken initial, procedural steps toward voiding the law.
On a party-line 52-48 vote Thursday, Republicans defeated a Democratic proposal that would have allowed a filibuster which requires 60 votes to end of any bill repealing the health care law unless it would also fully replace it.