A top Republican senator suggested Tuesday that White House staff take away President Trump's smartphone after he called for a possible government shutdown this fall.

"I think retrieval of his iPhone would be a good thing, and only staff-approved tweets after that," Sen Bob Corker, R-Tenn., said after a meeting with Vice President Pence in which other Republican senators complained to Pence about Trump's tweet.

Trump early Tuesday blamed GOP concessions in a $1 trillion spending bill on the 60-vote threshold for passing legislation in the Senate, which gives Democrats the power to block bills.

"Either elect more Republican Senators in 2018 or change the rules now to 51%." Trump tweeted. "Our country needs a good 'shutdown' in September to fix mess!"

Those who attended the closed-door GOP lunch with Pence in the Capitol said senators weren't happy with the tweet, and said it damaged efforts to find consensus within the party and with Democrats.

"That's just not constructive," said Corker, who said he was not among those who addressed Pence. "Those are the kinds of things that should never happen. It's damaging to our credibility, it's damaging to trust within the building."

Rep. Jeff Flake, R-Ariz., said "absolutely none of that" when asked if he agreed with Trump's call to end the 60-vote threshold. "He can say what he wants. This is the Congress. There is a separation of powers. We appropriate and authorize."

Flake said he did not believe Trump was threatening Congress or that he would truly send the government into a partial shutdown.

"He was probably just trying for leverage for when the next fiscal year comes up in September," Flake said. "But a government shutdown, there is no stomach for that."

Sen. John McCain, R-Ariz., said he wasn't very worried about Trump's tweet. "I've learned one lesson, and that's to pay attention to what he does rather than react to everything he says," McCain said.

Still, the Senate has been inching toward elimination of the 60-vote threshold. Senate Democrats took the first step in 2013 when they gutted the 60-vote requirement for lower court judges and executive branch nominees. Republicans pushed it further last month when they lowered the requirement from 60 to 51 for Supreme Court nominees.

The two moves have alarmed Senate traditionalists and the majority have signed onto a letter calling for restraint when it comes to the 60-vote requirement for passing legislation. But there are some senators who would at least consider it.

Rep. Richard Shelby, R-Ala., is among them. He told the Washington Examiner he would consider the rule change if Democrats block government funding legislation in the fall, which they will likely threaten to do if it includes conservative provisions.

"If the Democrats just threaten to shut down the government, it's worth the debate," Shelby said. "There is merit to both sides of that. I wouldn't close my eyes to anything that's not prohibited by the Constitution. And it's not."

Al Weaver contributed to this report