As party whip, Cornyn is second in the GOP Senate leadership. He is the overwhelming favorite to win his third term in office during November's general election.
Cornyn has been dubbed too moderate by a small group of tea party activists. He faced a last-minute challenge from the right by Stockman, a fierce conservative and House renegade.
But Stockman struggled to raise money. He did little organized campaigning, ignoring the media and alienating many top Texas grass-roots organizers.
Stockman even dropped completely out of sight for nearly three weeks in January - though it turned out he'd been part of an official overseas delegation.
Take ABC13 with you!
Download our free apps for iPhone, iPad and Android devices