Tuesday's debate at WFAA in Dallas may shape the July 31 runoff election pitting Lt. Gov. David Dewhurst against former state Solicitor General Ted Cruz.
Cruz is a tea party favorite and ex-ivy league debating champion. Dewhurst is the mainstream GOP choice, but has a halting speaking style.
They largely agreed on major issues during a pervious debate June 22.
Dewhurst won the May 29 primary by 10 percentage points but failed to capture an outright majority to replace retiring U.S. Sen. Kay Bailey Hutchison.
The race has become especially heated in recent days, with both campaigns accusing each other of launching character attacks.