Cornyn, asked about Herman Cain's floated nomination to serve on the Federal Reserve Board, said the "bigger issue" was that the White House needed to "consult" with Senate Republicans before making a nomination.

"I think the White House needs to consult with the Senate before they make nominations because it's not a given that everybody they nominate is going to be confirmed," Cornyn told reporters early Tuesday evening.

"So I think rather than have the embarrassment for the nominee and for the president or for senators, the thing I just encourage is there has to be consultation," Cornyn added.

The comments come amid concerns from Republican senators about Cain's potential nomination and questions about whether he could be confirmed by the Senate. Cornyn predicated on Tuesday that Cain could "probably" be confirmed.

Republicans hold a 53-seat majority, meaning if all Democrats opposed Cain, he would have to lose four GOP senators for his nomination to be blocked.

Cain previously served on the Federal Reserve Bank of Kansas City. He was also accused of sexual harassment in 2011 by four women, though he's denied the allegations.

The potential fight over the Fed seat come as Trump is stacking up the number of nominations that need to be made and sent to the Senate, paving the way for several heated fights in the chamber where his nominations have emerged as a political lightning rod.

Sen.(R-Texas) on Tuesday urged the White House to coordinate on nominations to avoid the "embarrassment" of the Senate rejecting one of's nominees, warning "it's not a given" that all will be confirmed.Some conservatives are floating former Kansas Secretary of State Kris Kobach (R) for the job.