"I haven't seen the letter," Rep. Steny Hoyer ,D-Md., said on Tuesday, according to The Hill. "But President Obama correctly … stated that, 'Look, we believe the Affordable Care Act is a very important piece of legislation which has given Americans better health, better access, more reliability. And if you have a bill … that improves upon all this, well, you know, maybe I could support it.'"

Trump, who since his election has swung radically between praising Obama and denouncing him as a failure, reportedly called the letter "beautiful."

Related: Group says don't repeal ACA, add more options for seniors

It remains unclear whether Trump has a clearly-defined health policy in mind as an alternative to Obamacare and what that might look like. He has talked broadly about a number of market-oriented health policies favored by conservatives, such as eliminating the prohibition on selling health plans across state lines and encouraging health savings accounts, but he also recently promised to provide insurance "for everybody."

Most analysts say it is hard to imagine a scenario in which the federal government can provide universal coverage without maintaining some of the funding provisions that Republicans have denounced — and which Trump targeted his first day in office with an executive order — such as the individual insurance mandate.

Republicans in Congress are also divided about how the Obamacare repeal should proceed and what should replace it.

Some conservatives, notably libertarian-leaning Sen. Rand Paul, R-Ky., advocate abandoning any promise of universal coverage and instead focusing on market-driven reforms that they say will make private health plans cheaper.

Other Republicans are more sensitive to the risk of undoing a system that provides coverage for millions and many are feeling pressure from the governors of their states to maintain the expansion of Medicaid that has boosted coverage by roughly 11 million.