WASHINGTON — House Republicans muscled through a stopgap bill Friday that would fund the government only if all spending for President Obama’s health care law is eliminated. Senate Democrats and President Obama quickly made it clear they had no intention of going along, putting the government on a course toward a shutdown unless one side relents.

The 230-to-189 party-line vote in a bitterly divided House set in motion a fiscal confrontation with significant implications — politically and economically — but with an uncertain ending. Without a resolution, large parts of the government could shut down Oct. 1, and a first-ever default on federal debt could follow weeks later.

Each side predicted that the other would be held responsible, but determined House Republicans knew they were taking a risk even as leaders of the party’s establishment warned about the threat of destructive political consequences.

Mr. Obama called House Speaker John A. Boehner on Friday evening but only to reiterate that he would not negotiate with him on raising the federal debt limit and said it was Congress’s constitutional obligation to pay the nation’s bills. Both sides described the call as brief and fruitless.