Mr. Trump was left to strike a balance between siding with House Republicans while also distancing himself from the details, with top aides conceding that the legislation needed modifications before it could pass the full Congress.

On Tuesday, the president talked with House leaders about revisions to address the concerns of the most conservative members, and to Republican senators who fear the measure headed to the House floor would be too costly for older residents.

The C.B.O. report clarified just who stood to lose the most under the Republican plan, which in effect would shift health insurance costs from younger, healthier Americans to older, sicker Americans.

Under current law, insurers cannot charge older adults more than three times what they charge young adults for the same coverage. The House bill would allow insurers to expand that to 5-to-1.

Senator Bill Cassidy, Republican of Louisiana, noted that Americans over 60 who earn a little too much to qualify for Medicaid would “have a hard time affording insurance” under the House plan, since insurance premiums would rise far higher than the modest tax credits on offer. “That’s not good,” he said.

The House bill includes large transition grants to the states that can be used to help cover people with pre-existing medical conditions, subsidize insurance purchases beyond the bill’s tax credits, or other interventions; some Senate Republicans would seek to make those bigger as well. Mr. Thune wants to revise the tax credits so that they would be focused more on lower-income people.