President Donald Trump and House Republican leaders would have been better served by attempting tax reform or boosting infrastructure spending before taking on a health-care overhaul, GOP Sen. Bob Corker told CNBC on Tuesday.

Trying to repeal and replace Obamacare was the "wrong place to start," said Corker, chairman of the Senate Foreign Relations Committee and a member of the Banking and Budget committees. "There are so many things we can agree together on. Infrastructure may be one. Tax reform may be one. We kind of led with our chin."

So until a health-care deal can be reached, the Tennessee Republican said he would like to see Americans who don't have the ability to buy insurance on Obamacare exchanges allowed to use their health subsidies to purchase coverage outside the marketplaces.

"That would begin to do away with some of the harmfulness that's accruing to Tennesseans and people all across our country that don't have a choice," he argued.

Vice President Mike Pence and two top White House officials late Monday reportedly made a new offer to the hardline conservative House Freedom Caucus, whose opposition spurred Speaker Paul Ryan to embarrassingly pull the GOP's Obamacare replacement bill last month.

Under the administration's offer, states would be allowed to apply for waivers from several coverage requirements imposed on insurers by former President Barack Obama's 2010 health-care law.

Last week, Corker tweeted a veiled swipe at Ryan for advising Trump not to work with Democrats on health care.

We have come a long way in our country when the speaker of one party urges a president NOT to work with the other party to solve a problem.

"Something like health care is best done in a bipartisan way," Corker told CNBC on Tuesday. But he said he recognizes the gulf between the Freedom Caucus and moderates. "It seems one side is really going to have to give for this to happen on the Republican side," he acknowledged.