Updated 7:01 p.m. | A behind-the-scenes debate over the timing of the final Senate votes on the continuing resolution was brought to light on the Senate floor Thursday by Sen. Bob Corker.

The Tennessee Republican wanted it to be clear that two Republican senators, Ted Cruz of Texas and Mike Lee of Utah, were objecting to an agreement moving up the final votes to tonight. The votes have been scheduled for the middle of the day on Friday.

“In talking earlier with the senator from Texas. It’s my understanding that the reason you don’t want to send a bill over to the House who could possibly put in place some very good policies for us here, is that you want the American people and the outside groups that you’ve been in contact with to be able to watch us tomorrow,” Corker said. “I’m just asking the question, is it more important to the senator from Texas and the senator from Utah that the people around the country watch this vote, or is it more important that we have a good policy outcome from our standpoint?”

The comments came in an exchange that came about because Majority Leader Harry Reid, D-Nev., made a unanimous consent request to queue up the votes leading to passage of the CR for later Thursday evening. Lee objected to that request, instead suggesting the votes come Friday.

“I was just over at the House and talked to members of leadership there, and they would like to get the piece of legislation from the Senate over there as quickly as possible so they could respond,” Corker said. “I think all of us on [the GOP] side would like to make some changes to the CR, changes that we believe to be good policy, and over on the House side we have a majority of Republicans.”

Cruz said he had also spoken with House Republicans, but he received a different message.

“I can tell you this morning I spoke to over a dozen House members who explicitly said it would be fantastic if Senate Republicans could show the same unity we did and vote against cloture, because Majority Leader Reid has filed an amendment to gut our language,” Cruz said.

Cruz, Lee and their supporters both inside and outside the Capitol are pushing their fellow Republicans to oppose a debate-limiting cloture motion, in a bid to muster 41 votes to send a signal that Reid shouldn’t be allowed to amend the measure with a post-cloture vote to fund the health care overhaul. The effort has the backing of a number of outside conservative and tea-party-affiliated groups.

It is true that imposing limits on the debate will also allow Reid to get a vote on his germane amendment without needing 60 votes.

That’s created a tactical disagreement among Republicans. Corker’s long been critical of the strategy favored by Cruz and Lee.

Speaker John A. Boehner, R-Ohio, said earlier Thursday that the House intended to make changes to the measure.

The Corker-Cruz video clip is below: