Trump, according to The New York Times, demanded a vote on repealing the Affordable Care Act "probably some time next week," and said "the replace will be very quickly or simultaneously, very shortly thereafter."
"Long to me would be weeks," Trump said. "It won't be repeal and then two years later go in with another plan," he said, referring to proposals by some Republicans to "repeal-and-delay."
The Times noted that it "is very likely impossible" that a replacement plan could be adopted that quickly since GOP leaders in Congress are not close, at all, to crafting a replacement to the ACA. Obamacare in the past six years has driven the nation's uninsured rate to record lows, as 20 million people have gained health coverage.
Trump called Obamacare "a catastrophic event."
"I feel that repeal and replace have to be together, for very simply, I think that the Democrats should want to fix Obamacare. They cannot live with it, and they have to go together."
Trump's latest comment on Obamacare is sure to shake up the political debate over replacement even more.
Earlier Tuesday, a new analysis found that more than half of Obamacare customers nationwide live in a congressional district represented by a Republican.
Of 11.5 million Obamacare enrollees nationally as of March, a total of 6.3 million live in Republican-held districts, according to the Kaiser Family Foundation study.
The remaining 5.2 million customers live in districts held by Democrats, the study found.
Also Tuesday, the Obama administration announced that more than 11.5 million people so far have purchased health plans for 2017 sold on Obamacare exchanges nationally, a slight gain in the enrollment pace seen during the same period last year.
The new data were released a week after Republicans in the new 115th Congress took steps toward repealing key parts of the Affordable Care Act.
Since then, there has been growing debate within the GOP about whether the ACA should be repealed without a simultaneous replacement for Obamacare.
Such a plan could, to at least some extent, mitigate the loss of coverage and increases in individual plan premiums that other analyses have found would ensue if the ACA provisions were repealed with no backup.
To pass repeal through the process known as reconciliation, the Republican-led Senate, which holds 52 seats, needs just 50 votes. But to ensure a replacement plan is passed without being held up by a filibuster, Republicans would need 60 votes — presumably eight or more which would have to come from Democrats whose party passed the ACA into law.
Democrats so far have shown no willingness to support a replacement plan.
The easier road for repeal led Republicans to consider doing that first and then dealing with a replacement, which could take several years.
But that strategy has been challenged as health-insurance experts and others have warned that large numbers of people could lose coverage and prices could rise sharply if a replacement is delayed by years, as some Republicans have suggested.
That in turn has raised fears that Republicans could suffer politically if they repealed Obamacare without replacing it.
In recent days, a number of senators have wavered on the idea of of "repeal-and-delay."
On Monday, five Republican senators, including Sen. Bob Corker, R-Tenn., submitted an amendment that would delay the deadline for a Senate committee to draw up a repeal bill from Jan. 27 to March 3.
Another of the five, Sen. Rob Portman, R-Ohio, said that while he supports repeal, "Congress also should thoughtfully consider how we replace Obamacare, and we can do so by ensuring we go through the committee process."
"As we do so, we must ensure that Americans are able to retain their health care during the transition to a new system," Portman said."This amendment will ensure that we move forward with a smart, responsible plan to replace the law as quickly as possible."
Also Monday, Trump's incoming chief of staff Reince Priebus, his Treasury Secretary-designee Steven Mnuchin and senior Trump advisers Steve Bannon and Jared Kushner huddled with House of Representatives Speaker Paul Ryan in Ryan's office to discuss repeal and replacement.
"Still thinking it through," Bannon said, according to a tweet from Associated Press reporter Erica Werner.
Priebus was overhead saying, as he left the Capitol, "We have a huge challenge here, it was better tonight," according to another tweet from Werner.