Senate Republicans are getting tired of being caught off-guard by President Trump on key issues like health care and controversial nominees like Herman Cain, and say there needs to be more consultation from the White House.

Trump's allies say they often find out about the president's plans on Twitter or through media reports, making it almost impossible to offer the White House any advice before major decisions are announced.

"When names are floated, you guys come around and ask, 'What about this person? What about that person?'" Sen. John Cornyn (R-Texas), a member of the GOP leadership team, told reporters Wednesday, saying he would like to see "more communication and collaboration."

"This is a nontraditional presidency, and the president now figures he doesn't need a lot of advisers because he wants to do it himself. But there's a lot of informal mechanisms and avenues for sharing information that are not really working very well now," he added.

Senate Majority Leader Mitch McConnell (R-Ky.) and Senate Judiciary Committee Chairman Lindsey Graham (R-S.C.) said Thursday that they agreed with Cornyn that there needs to be more communication between the White House and congressional Republicans.

"I think that's good advice," McConnell told reporters when asked about his colleagues' desire for more consultations.

"I agree with that," Graham told The Hill.

GOP senators didn't get any advance notice on several of Trump's recent high-profile moves: his decision to rebrand the GOP "the party of health care" and his intention to nominate controversial partisan figures like Cain and Stephen Moore to serve on Federal Reserve Board.

McConnell had to tell Trump in a follow-up phone call on April 1 that Senate Republicans did not intend to move a health care reform package before the 2020 election. Trump had surprised GOP lawmakers a week earlier when he told them in a private lunch meeting to put together legislation to replace the 2010 Affordable Care Act, which Trump's Justice Department is opposing in court.

A few days later, Trump caught GOP lawmakers flat-footed again when he said he planned to nominate Cain, a 2012 GOP presidential candidate who dropped out of the race when sexual harassment allegations emerged, to a top Fed post.

Floating Cain's nomination came on the heels of Moore, another highly controversial Fed pick. After Trump announced his intention to nominate Moore - the founder of the conservative Club for Growth, which has spent millions of dollars in ads against Republican and Democratic candidates - it was revealed that he owed more than $75,000 in unpaid taxes and penalties.

Trump announced his planned Fed nominees before checking in with the Senate, and it now appears that Cain doesn't have enough votes to win confirmation.

Sen. Kevin Cramer (R-N.D.), a member of the Senate Banking Committee, told reporters Thursday that "if I had to vote right now, there's no way I could vote for" Cain. He became the fourth Republican to announce likely opposition to the prospective nominee, joining Sens. Mitt Romney (Utah), Lisa Murkowski (Alaska) and Cory Gardner (Colo.).

Republicans control 53 seats and Democrats would likely vote in unison against Moore and Cain.

McConnell on Thursday said the administration should check in with Senate Republicans to see if nominees who are likely to be controversial will be able to muster enough GOP votes before floating their names.

"There are two things the administration ought to consider before nominating someone. First, obviously, background check. And second, likelihood of confirmation," he said. "Generally better to check that out in advance before you send a nomination up."

Trump's threat to close the southern border was another curveball GOP senators had to deal with in recent days.

McConnell warned doing so would be "catastrophic," while Cornyn said there would be "unintended consequences."

The president later backed off the threat.

Graham said this week that he and his colleagues should find out what Trump has planned from the White House, as opposed to learning about it in the news.

Instead of GOP lawmakers "reading about stuff in the paper," White House officials "should call the appropriate committee chairmen who are going to have to confirm these nominees and say, 'Here's what we're thinking,'" Graham said.

"I think that serves you better - to collaborate and run names past people," he added. "It's certainly up to the president to do what he would like, but I think a process of a consultation would inure to the benefit of the White House in the Senate - instead of just reading about it every day."

Graham said he was "completely surprised" by Trump's announcement that he would put Moore and Cain on the Fed.

"These will be challenging nominations," he said.

A senior GOP lawmaker, who requested anonymity to speak about frustrations with Trump, said that consultation on nominees is especially important at a time when it has become very difficult to secure Democratic votes for controversial picks.

"On nominees, it's clear that there's not going to be much or any bipartisan cooperation, so it would really be helpful if ahead of time they would check with us to see if we have 51 votes," the lawmaker said of the White House.

But while Senate Republicans are frustrated, they realize that Trump, 72, is set in his ways and not likely to change too much.

"The president, he's got his own style of operating. We're adapting to it, and we kind of just expect that we're going to get surprised once in a while," said Senate Republican Whip John Thune (S.D.).

"Every president has a different way of operating," he said, noting that when Republicans controlled the White House under former President George W. Bush, "Twitter wasn't a form of communication."

Thune said it's helpful when McConnell and Trump talk, and he urged the president to keep the GOP leader in the loop.

"The more the president can give a heads-up, the more Sen. McConnell can provide input and guidance and let the president know what's passable and what's not," he said.

Thune said he didn't have any advance notice on Cain's nomination, adding "sometimes the president in terms of his style of operation tends to be more freewheeling."

"That's something we've just had to learn to adapt to," he said.