Two days after Republicans across the country suffered a drubbing, dragged down by their opposition to abortion rights in the off-year elections, G.O.P. leaders on Capitol Hill appeared not to have gotten the memo.

House Republicans tried on Thursday to use a financial services spending bill to chip away at a District of Columbia law aimed at protecting employees from being discriminated against for seeking contraceptive or abortion services. Tucked inside the otherwise dry bill was a line barring federal funds from being used to enforce that law.

But minutes ahead of an expected vote, Republicans were forced to pull the legislation from the floor. Mainstream G.O.P. lawmakers from competitive districts — concerned that their party’s opposition to abortion rights has alienated women — appeared unwilling to support the abortion-related restriction, sapping the measure of the votes necessary to pass.

It was the latest reflection of the deep divisions among Republicans that have prevented them, for the moment, from coalescing around a strategy for averting a government shutdown.

But this time, it was also an illustration of yet another disconnect — between a small group of Republicans in Congress who are trying to pivot away from an anti-abortion message that voters have rejected and a much larger coalition, including the party’s leaders, who are doubling down.

Tuesday’s election results drove home to some Republicans in Congress what they already know and fear — that their party has alienated critical blocs of voters with its policies and message, particularly on abortion. And the results stiffened their resolve to resist such measures, even if it means breaking with the party at a critical time in a high-stakes fight over federal spending.

“The American people are speaking very clearly: There is no appetite for national abortion law,” Representative John Duarte of California, a Republican who represents a district that President Biden won in 2020, said on Thursday. “And there’s enough of us in the Republican Party that are going to stand against it.”