WASHINGTON — Alaska Sen. Lisa Murkowski on Aug. 1 joined a bipartisan coalition to introduce a bill that would protect abortion and contraception access.

The measure faces an uncertain future in a Senate that failed to pass a broader measure enshrining abortion rights in May. It also comes as Murkowski faces reelection this fall, with abortion emerging as a key issue in that campaign.

Despite the bill’s bipartisan co-sponsors — Democrats Tim Kaine, of Virginia, and Kyrsten Sinema, of Arizona, and Republicans Susan Collins, of Maine, and Murkowski — it is unlikely to clear the 60 vot...