Dewhurst has held the powerful lieutenant governorship since 2003 but is locked in a fierce battle for the Republican nomination to replace retiring U.S. Sen. Kay Bailey Hutchison with former state Solicitor General Ted Cruz - a tea party favorite.
The pair face a July 31 runoff election after neither won a majority of the votes cast during last month's primary, though Dewhurst came close.
Dewhurst declared Saturday that "Washington is a disaster" and said he'd make the federal government more like Texas.
His speech to the convention in Fort Worth came shortly after Cruz's, and struck a more-subdued tone. But Dewhurst also largely avoided boos from tea party supporters.