Story highlights Top Republicans are looking at a mix of smaller bills

Republicans are concerned that a full-scale bill will become unwieldy

Washington (CNN) Senate Majority Whip John Cornyn of Texas said Thursday Republicans won't offer a comprehensive bill to replace Obamacare, saying instead that the GOP will try to enact individual health care measures.

Republicans are concerned that a full-scale bill will become unwieldy and will be difficult to attract support.

So instead, top Republicans are looking at a mix of smaller bills that could attract bipartisan support in Congress and executive actions that could be pursued by President-elect Donald Trump and Rep. Tom Price if he's confirmed as Health and Humans Services secretary.

"We're not going to do a comprehensive bill. We are going to do it in a step-by-step basis," Cornyn, the No. 2 Senate Republican, told CNN. "If I've learned anything since I've been here in the Senate, big comprehensive bills are not the way to go."

Asked which aspect of health care Republicans would tackle first on a replacement measure: "That hasn't been decided."

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