State Senator Leticia Van de Putte’s announcement on Saturday that she is running for lieutenant governor, adding a second woman to a ticket led by State Senator Wendy Davis, is enhancing Texas Democrats’ hopes that they could see their first statewide victory since 1994.

The Democrats are pinning their strategy in part on women, particularly those in the suburbs, who early polling numbers suggest might not have their minds made up, and could be persuaded by the summer’s divisive debate over abortion legislation.

“What we know from the outcome of this summer is that women were paying attention and women were watching,” Ms. Van de Putte said. “It wasn’t just about that bill. It wasn’t just about health care. It was about not being valued.”

But Republicans say they are holding fast to this demographic, which has trended conservative in past elections.