(CBS) — President Trump is expected to announce his choice for the Supreme Court Monday night, and the moment the nominee is announced, the battle for confirmation will begin. Republicans hold a narrow one-seat majority in the Senate.

Texas Republican Sen. John Cornyn will be in the room when the president reveals his choice. Like many of his GOP colleagues, Cornyn is already delighted by the short list.

“I honestly think that if it’s one of the four, I think that they will be relatively easily confirmed,” Cornyn said.

But even as Republicans celebrate, they know a bitter fight lies ahead. Democratic leader Sen. Chuck Schumer set the tone on Monday, warning women’s rights are at stake.

“That’s what we’re up against here,” Schumer said. “That’s why America is on tenterhooks, so worried about any choice from this list.”

Pennsylvania Democratic Sen. Bob Casey, up for reelection in November, announced on Monday that he will vote against the president’s nominee no matter who it is, and called the selection process “corrupt.”

“The Democrats are not going be happy with anybody,” said Utah Republican Sen. Orrin Hatch.

He’s rooting for Judge Amy Coney Barrett, whose conservative views might draw the most ire from Democrats.

“She’s really outstanding,” Hatch said. “There’s no question about it and I know the Democrats would go into orbit over it, make it a very tough set of hearings but she can handle it.”