Dewhurst wouldn't say which bills he was talking about, but made his remarks Sunday night as the House debated a bill with tough new restrictions on abortion.
Dewhurst wouldn't predict when a second special session might start.
Other bills facing a midnight Tuesday deadline and a possible filibuster by Democrats include a major transportation funding bill and one to create new punishments for 17-year-olds convicted of capital murder.
Dewhurst suggested House members could remove a provision that bans abortion after 20 weeks and send the bill straight to Perry to sign into law. The Senate passed the bill without that provision.
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