Thompson, secretary of Health and Human Services during the George W. Bush presidency, said the health law is "spiraling downward," but waiting for it to implode would be a "catastrophe for people who have Obamacare" as premiums continue to rise and more insurers pull out "because they can't make any money."
In the wake of the failure of the House GOP's American Health Care Act, White House Budget director Mick Mulvaney on Sunday reiterated President Donald Trump's desire to move on to other legislative priorities, such as delivering on promises of tax cuts.
But Thompson, formerly governor of Wisconsin, warned on "Squawk Box" against that strategy due to "big issues" coming up for lawmakers sometime in May.
"They're going to have to vote on whether to continue the [Obamacare] subsidies or not," he said. "Health care is not something they're going to be [able] to put to the side and watch it die a slow death."
Facing resistance from the House Freedom Caucus, which Mulvaney helped found when he was in Congress, House Speaker Paul Ryan dropped the plan on Friday afternoon. Mulvaney, on NBC's "Meet the Press," chalked up the health-care failure to Washington's being "more rotten" than Trump thought.
Thompson said Trump and Republican leaders need to "regroup" and educate rank-and-file lawmakers and the American public on the merits of fixing Obamacare now. "It was the right bill … [but] not the total bill," he said, adding that Ryan was "very upfront and said 'this is a three-legged stool,' and the AHCA was just the first step.
"All of it together would have worked," Thompson said. "The problem was the first one [AHCA] had a lot of consequences because it was dealing with the budget reconciliation. And not too many people understood there was a second and a third act to follow that would have fixed some of those problems."