WASHINGTON — A meeting Friday between President Trump and Ohio Gov. John Kasich, his former rival in the Republican primaries, had no set agenda. But Kasich came armed with one anyway: his hope to blunt drastic changes to the nation’s health-care system envisioned by some conservatives in Washington.

Over the next 45 minutes, according to Kasich and others briefed on the session, the governor made his pitch while the president eagerly called in several top aides and then got Health and Human Services Secretary Tom Price on the phone. At one point, senior adviser Jared Kushner reminded his father-in-law that House Republicans are sketching out a different approach to providing access to coverage. “Well, I like this better,” Trump replied, according to a Kasich adviser.

The freewheeling session, which concluded with the president instructing Price and Chief of Staff Reince Priebus to meet with Kasich the next day, underscores the unorthodox way the White House is proceeding as Republicans work to dismantle the Affordable Care Act and replace it with something else. The day after Kasich delivered his impromptu tutorial, Trump spent lunch discussing the same topic with two other Republican governors with a very different vision: Scott Walker of Wisconsin and Rick Scott of Florida.

Scott said Sunday that he used the lunch to press for principles he has pushed publicly, such as financial compensation for states that did not expand Medicaid under the ACA and the importance of providing competition and cutting required benefits to allow people to “buy insurance that fits them.”

While leaving most of the detail work to lawmakers, top White House aides are divided on how dramatic an overhaul effort the party should pursue. And the biggest wild card remains the president himself, who has devoted only a modest amount of time to the grinding task of mastering health care policy but has repeatedly suggested that his sweeping new plan is nearly complete.

This conundrum will be on full display Monday, when Trump meets at the White House with some of the nation’s largest health insurers. The session, which will include top executives from Blue Cross and Blue Shield, Cigna and Humana, is not expected to produce a major policy announcement. But it will provide an opportunity for one more important constituency to lobby the nation’s leader on an issue he has said is at the top of his agenda.

Democrats and their allies are already mobilizing supporters to hammer lawmakers about the possible impact of rolling back the ACA, holding more than 100 rallies across the country Saturday. And a new analysis for the National Governors Association that modeled the effect of imposing a cap on Medicaid spending – a key component of House Republicans’ strategy – provided Democrats with fresh ammunition because of its finding that the number of insured Americans could fall significantly. Trump, for his part, continues to express confidence about his administration’s ostensible plan.