Despite the hype surrounding Texas Democrat Wendy Davis’s run for governor, the chairman of the Democratic Governors Association didn’t include her state in a list of top targets in 2014.

Ms. Davis, a state senator, gained national acclaim for filibustering a bill last year that increased regulation of abortion clinics and banned abortions after 20 weeks of pregnancy. Polls show Republican nominee Greg Abbott with a double-digit lead in the state, which hasn’t elected a Democrat since 1994.