But the new top ranking Republican on the Senate Judiciary Committee, Sen. Jeff Sessions, isn't one of them.
He admits the American public may have some concerns about a gay nominee and hopes the president won't play politics with his pick.
"Republicans don't believe in identity politics," Sessions told FOX News. "We just don't believe in that kind of quota approach to life. Let's just bring the nominee up and make sure that they treat everybody fairly regardless of what kind of persuasion they may have."
On Monday, top administration officials met with gay rights leaders on the heels of complaints from some prominent gay rights organizations that the president hasn't nominated anyone openly gay to a top position, the White House said.
"He does not want this conversation, this argument, this screaming match, over his judicial nominee," GOP strategist Marjorie Dannenfelser told FOX News. "And he should try to avoid it by not finding a nominee that makes those issues central."
Chuck Wolfe, president of the Gay & Lesbian Victory Fund, said, "There are some saying that it's a bridge too far today and I think pretty much the American people have said that folks who are saying things like that are out on the bridge all by themselves."
Both sides of this debate say they believe Sessions when he says an openly gay nominees would get a fair shake and that the real fight will come down to whether or not that nominee would bring a personal agenda to the bench.