But Democrats were confident many colleagues across the aisle would come to regret this vote, particularly in an election cycle where the president’s party is typically on the defensive and when Republicans will need to protect nearly two dozen districts carried by Hillary Clinton last year. Those districts alone, including some in places like California, Texas and Illinois, are almost enough to determine who runs the House.

“Republicans kicked a hornet’s nest, and it is not too soon to begin saying goodbye to some of my Republican colleagues from moderate districts, because this will cost them dearly,” said Representative Luis V. Gutiérrez, Democrat of Illinois.

The 2018 campaign is only now beginning, and the political climate is highly volatile. The outlook for the House bill in the Senate is uncertain, and it could be significantly rewritten. But Democrats believe that the potential ramifications of the House-passed measure — millions losing insurance coverage, a diminished array of benefits, no definite guarantee of coverage for those with pre-existing conditions — provide them with powerful ammunition against Republicans.