AUSTIN, Texas—Wendy Davis, a state senator from Fort Worth, became an overnight sensation among Democrats and abortion-rights supporters after staging a marathon filibuster Tuesday that helped kill legislation that would have restricted abortions in Texas.

But her victory may be short-lived, as Republican Gov. Rick Perry on Wednesday called the legislature, which usually meets only every two years, back into another special session starting Monday to reconsider the abortion bill and other unfinished business.

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