WASHINGTON — Shortly after President Trump took office, Senator Mitch McConnell of Kentucky, the majority leader, met privately with his colleagues to discuss the Republican agenda. Repealing the Affordable Care Act was at the top, he said. But replacing it would be really hard.

Mr. McConnell was right.

The many meetings Republicans held to discuss a Senate health care bill have exposed deep fissures within the party that are almost as large as the differences between Republicans and Democrats. Elements of a bill that passed the House this month have divided Republicans.

Mr. McConnell faces an increasingly onerous math problem. He can afford to lose only two Republicans if he is to get a bill through the Senate, and that would require the help of Vice President Mike Pence, who would have to cast the tiebreaking vote. But at least three senators in the party are diametrically opposed to the views of at least another three, so the path to agreement is narrow.

Republicans are roughly split over whether the expansion of Medicaid under the Affordable Care Act should be rolled back or continued, at least in the short run. They disagree about how the federal government should grant states more control over setting insurance standards.