The Supreme Court’s refusal Monday to block a decision nullifying Pennsylvania’s congressional map leaves the state facing a confused political landscape and raises the prospect of new district lines that could give Democrats a boost in their push to retake the U.S. House.

With Pennsylvania’s primary a little more than three months away, candidates and voters still don’t know which districts they will be in. The state Supreme Court has ordered legislators to come up with a new map within days, vowing to draw one itself otherwise,...