On Tuesday, Trump said, "Let Obamacare fail; it'll be a lot easier."
"We'll let Obamacare fail, and then the Democrats are going to come to us, and they're going to say, 'How do we fix it? How do we fix it?' Or, 'How do we come up with a new plan?'" he told reporters.
However, on Wednesday the president called for renewed efforts to draft new legislation instead of letting Obamacare implode. He said senators should stay in Washington, D.C., to hammer it out before leaving for the August recess.
"We have no choice. We have to repeal and replace Obamacare. We can repeal it, but the best is repeal and replace," Trump said.
Following Trump's comments, Senate Majority Leader Mitch McConnell, R-Ky., said the Senate would proceed next week with a vote on a motion to move ahead with a repeal bill. While the proposal doesn't include a replacement plan, it could be amended, he said.
According to the Congressional Budget Office, repealing many Obamacare provisions would lead to 27 million uninsured people in 2020. That figure would climb to 32 million by 2026, the CBO said in its new report.
"That means 1 in 10 Americans will lose their insurance if this bill is repealed," Molina said.
He said stabilizing the Obamacare marketplace requires insurance subsidies to be funded. He said there should be a reinsurance pool so that health plans don't have an incentive to avoid costly patients. Plus, the mandate needs to be enforced, he said.
"You can't expect health insurance companies to insure people and have guaranteed access to insurance and not have people required to sign up. You can't expect them to only insure sick people," said Molina.
— CNBC's Christine Wang and Jacob Pramuk contributed to this report.