WASHINGTON—Senate Republicans on Wednesday blocked Democrats' effort to undermine the Supreme Court's Hobby Lobby decision, ending a round of partisan jousting aimed at capturing women's votes in the fall.

A bill from Senate Democrats designed to restore employers' responsibility to provide contraception coverage under the Affordable Care Act was defeated 56-43 on a procedural vote. It sought to prevent companies from using a religious-freedom law to avoid complying with a requirement to cover all forms of contraception approved...