WASHINGTON—House Republicans are struggling to advance their year-end tax bill, with just a few legislative days to go until they relinquish the majority to the Democrats.

GOP leaders decided late Thursday that the measure, already mired in partisan disagreements and facing a crowded Senate calendar, wouldn’t get scheduled for a House vote on Friday, leaving its fate uncertain.

The bill’s author, Rep. Kevin Brady (R., Texas), said Friday that lawmakers would continue working on it with the hope of voting next week.

Republicans packed the catch-all legislation with provisions that for the most part enjoy broad support. Those include proposals to encourage retirement savings, extend lapsed tax breaks, improve taxpayer assistance at the Internal Revenue Service and aid disaster victims.

But the bill doesn’t contain revenue-raising offsets, and it includes technical corrections to last year’s tax law that most Democrats don’t want to accept for free. The longer the House waits to vote, the harder it becomes to cut a final bipartisan deal before Congress leaves Washington for the year.