Rather than respond, Lee yielded to Cruz.
All it takes is one senator to object to delay a vote and Lee did that. Because of his objection, a technical vote on a stopgap funding measure that also cuts all money for the Affordable Care Act will take place Friday afternoon instead of Thursday night.
The stalling tactic brought a strong rebuke.
Senate Majority Whip Dick Durbin, D-Ill., said Lee's move increased the chance of a government shutdown and that would hurt among others active military soldiers who would go without pay if that happens.
"They'll be paid but their paychecks will be delayed," Durbin said. "But what it means is they'll have to contact their wives and spouses back home, come Tuesday if this Cruz and Lee delay continues, they'll have to contact them and say, 'Honey, it'll be a little difficult this pay period. It doesn't look like we'll be getting a paycheck because Congress has shutdown the government.' "
"Why do these two senators these two senators believe this is in the best interest of America?" Durbin asked.
"Stand their ground" • Cruz and Lee had previously urged their House colleagues to pass the temporary budget resolution that halts any cash for implementing Obamacare. House Republicans followed through but Senate Republicans don't have the votes to stop Democrats from restoring the funding so Lee and Cruz have been trying to block action on the bill they support.
Senate Majority Leader Harry Reid, D-Nev., called the one-day delay engineered by Lee a "big, big charade" that could endanger Congress' ability to get a bill passed by deadline.
Later, Lee's spokesman Brian Phillips disputed suggestions that the timing drama is about publicity.
"The implication that this is about any one senator is absurd," Phillips said. "It's a lazy personal attack and totally baseless."
Rather, the delay is needed to translate to the public what is going on under the complex rules of Congress, he said.
"The American people are tired of the games that hide the true meaning of these votes. And so we're forced to explain it to them as best we can, and that takes time."
Cruz told a group of reporters and bloggers on a conference call earlier Thursday that the House should continue to fight to end funding for Obamacare if, as expected, Senate Democrats restore that money .
"House Republicans can, and I believe should, continue to stand their ground," Cruz said. "If the House holds firm, Harry Reid has no ability to muscle the House of Representatives if they stand their ground."
House Republican leaders appear to have moved to a different tactic and are already working on a counter offer on the budget that doesn't end funding for the health care law. Some members didn't appreciate Cruz's suggestion.
"Get out of this mess" • "The game is not over in the Senate. Go fight those fights," said Rep. Jason Chaffetz, R-Utah. "We'll do the right thing in the House."
Rep. Rob Bishop, R-Utah, said: "I get frustrated when people keep telling me to hang in there and do something, when it is not moving over there. I want the Senate to hang in and do something."
All four of Utah's House members Chaffetz, Bishop and Reps. Chris Stewart and Jim Matheson voted for the bill that stripped out the health-care funding.
"I've voted 41 times to defund. I'm of the realization that probably won't happen," Chaffetz said. "But I do think delaying Obamacare for a year has a more realistic possibility of finding common ground."
He said the House doesn't plan to just "swallow what the Senate sends up."
But that may depend on when the Senate acts on the bill. With the delay pushed by Lee and Cruz, the Senate will begin voting Friday and could send legislation back to the House over the weekend.
Sen. Orrin Hatch, R-Utah, has announced that he would vote to end debate on the House bill but said he will miss that vote Friday because of a family responsibility.
He lamented that Democrats refused to budge when it comes to President Barack Obama's signature health law, which opens insurance exchanges beginning Oct. 1.
"Republicans have given them every chance to get out of this mess and they seem to want to keep their feet right in the mess," he said.
Matheson was one of only two Democrats who supported the effort to defund Obamacare. He says it's time to switch gears and simply pass a bill that keeps the government operating. He worries that any attempt to amend the bill that the Senate passes will result in a shutdown.
"I've always said it is a mistake for Congress to shut down the government," he said. "Assuming the bill is reasonable, sure, I'd vote to keep the government going."