WASHINGTON — In an embarrassing setback, House Republicans abruptly decided Wednesday to drop planned debate of a bill criminalizing virtually all late-term abortions after objections from GOP women and other lawmakers left them short of votes.

The decision came on the eve of the annual March for Life, when thousands of anti-abortion demonstrators stream to Washington to mark the anniversary of the 1973 Supreme Court decision that legalized abortion. It also came with GOP leaders eager to show unity and an ability by the new Republican-led Congress to govern efficiently.

Republican leaders had planned on Thursday House passage of the legislation, which would ban most abortions after 20 weeks of pregnancy.

But they ran into objections from women and other Republican lawmakers unhappy that the measure limited exemptions for victims of rape or incest to only those who had previously reported those incidents to authorities.

The rebellious lawmakers argued that put unfair pressure on women who often feel shame or fear retaliation if they report those assaults.