The three senators he has chosen to lead the effort — Bill Cassidy of Louisiana, John Barrasso of Wyoming and Rick Scott of Florida — have so far also declined to point to many specifics. When asked about an Obamacare replacement this week, they mentioned their more modest bills to reduce health care costs in the emergency room and at the drugstore. (A fourth senator the president has mentioned, the majority leader, Mitch McConnell of Kentucky, has been even more clear that he has little interest in pursuing comprehensive health care legislation.)

One clue to Mr. Trump’s thinking is the choice of Mr. Cassidy. Along with Senator Lindsey Graham of South Carolina, he was the author of a legislative plan that received some scrutiny in 2017 but never came up for a vote. Another hint can be found in the president’s own budget, released just before his reinvigorated health care push. A third is a draft proposal developed by a group of conservative Washington policy groups.

The Graham-Cassidy bill

The president has spoken fondly several times about this proposal, which did not have enough support in Congress to advance to a vote. It would eliminate current programs funding Obamacare’s Medicaid expansion, which covers the working poor, and insurance subsidies helping low- and middle-income Americans buy their insurance. Instead, that money would be grouped together, then parceled out to states to use in the service of health care programs they favor.

The legislation attaches some rules to how the money can be used — it must go toward health care, for example — but its main goal is to provide states with maximum flexibility to develop local and innovative solutions. (Some experts worry that states could struggle to develop such plans on the bill’s abbreviated timetable.)

That flexibility would allow states, if they so chose, to waive Obamacare’s rules that plans must cover a standard set of medical benefits, and that insurers must charge the same prices to customers with different health histories. It would be easy for states to circumvent current protections for Americans with pre-existing conditions. That ability would be at odds with the president’s recent promises to protect such rules.