Sen. Kay Bailey Hutchison (R) should stay in the Senate if she falls short in her bid to become governor of Texas, Sen. John Cornyn (R-Texas) said Wednesday.

Cornyn, the chairman of the National Republican Senatorial Committee (NRSC), said it was his hope that Hutchison would stay in the Senate until her term ends in 2012 if she loses her primary bid against incumbent Texas Gov. Rick Perry (R).

"My hope is that she'd stay on and serve the remainder of her term," Cornyn told The Hill in a brief interview.

Hutchison has been waging an intense bid to unseat Perry for months, but seems likely to fall short of succeeding in the March 2 primary. Hutchison could still force a runoff primary against Perry, setting up the prospect of an even more intense battle.

Hutchison had said she may resign her Senate seat, for which her term ends in the 2012 cycle, had she won her gubernatorial race. Some Republican and Democratic candidates have begun organizing campaign infrastructures in case Hutchison were to resign.

It's not clear when or if Hutchison might resign her seat, and Cornyn said he doubted his colleague would have considered the issue yet because, the NRSC chairman said," she's probably confident she's going to win."

"There's a lot up in the air right now," said Cornyn, who hasn't taken a position in the race. "We'll just take it one step at a time."