At left, Sen. Bob Corker speaks in Murfreesboro, Tenn., Aug. 6, 2013; at right, Sen. Ted Cruz speaks in Ames, Iowa, Aug. 10, 2013. (Erik Schelzig/AP Photo | Justin Hayworth/AP Photo)

Tension spilled over on the Senate floor Thursday as lawmakers squabbled over the timing of a vote to avert a government shutdown.

But it wasn't a Democrat vs. Republican fight. It was Republican vs. Republican.

Senate Majority Leader Harry Reid wanted to accelerate consideration of the continuing resolution by setting a vote for Thursday night. But Sens. Ted Cruz, R-Texas, and Mike Lee, R-Utah, objected, prompting Sen. Bob Corker, R-Tenn., to accuse the Texas senator of trying to gin up publicity over the vote.

"I'm understanding the reason we're waiting is that y'all have sent out [press releases] and e-mails and you want everybody to be able to watch," Corker said. "It just doesn't seem to me that that's in our nation's interest."

Cruz turned the tables on Corker, saying the Tennessee senator's vote on cloture on Friday will align with Democrats. Cloture is the procedure to bring a debate to a close, allowing a vote to take place.

"Why is Majority Leader Harry Reid going to vote the same way you're proposing to vote? Why is every Democrat in this chamber going to vote the way you're proposing to vote?" Cruz asked.

The fight highlighted a growing tension between many Republicans in the Senate and Cruz, whose 21-hour overnight speech in the Senate this week rankled some of his Republican colleagues.

Senate leadership wanted to move forward with the bill Thursday night to give the House more time to work on it and avoid a government shutdown, but Senate rules say a single senator can raise an objection to timing. While Reid placed the blame on Republicans for the stall, Corker pointed out that it was not all Republican senators who opposed the timing, just Cruz and Lee.

"It's not the Republican side that's asking to stall. We only have two Republican senators that are wanting to push this off," he said.

The Senate will hold its final votes on the continuing resolution on Friday afternoon, sending the bill to the House over the weekend as a government shutdown looms on Oct 1.