The Democrat from New Mexico presented the plan Monday morning to Gorsuch, President Donald Trump's nominee for the Supreme Court, as well as to Gorsuch's team of White House aides and former Sen. Kelly Ayotte, who's been attending Gorsuch's meetings with senators.
His proposal is for Trump to meet privately with Supreme Court justices who are interested in retirement. If one of those justices decided they would be willing to retire, and if Trump promises to nominate Garland, President Barack Obama's unconfirmed former SCOTUS pick, in their place, then the retiring justice would submit a letter of resignation contingent on that promise.
Then, both Garland and Gorsuch would be voted on simultaneously.
It's a far-fetched idea, and Udall told reporters he got no response or comment from Gorsuch's team in the room. But he added that he's been talking to other senators about it.
The White House appeared to dismiss the idea Monday.
"The President is focused on having the Senate confirm Judge Neil Gorsuch for the only open seat on the Supreme Court," a White House spokesperson said when asked about the proposal.
The idea closely follows a plot line from an episode of "The West Wing" television show. In season 5, episode 17, "The Supremes," a spot on the Supreme Court opens up and the White House works out a deal with another justice to retire so they can replace him with both a liberal justice while Republicans can get their pick of a more conservative justice.
Jennifer Talhelm, communications director for Udall, told CNN that the senator did not get the idea from the West Wing, and that while he has maybe seen an episode or two, he doesn't watch the show.
She said Udall has wanted to see Trump pick Garland all along, and his more recent idea came after he was speaking with a constituent who said they'd like to see both Garland and Gorsuch on the Supreme Court.
Speaking to reporters, Udall also recalled the time that President Lyndon B. Johnson wanted his adviser Abe Fortas on the Supreme Court, so he persuaded Justice Arthur Goldberg to retire by promising him the position of ambassador to the United Nations.
So what would be Trump's motivation to move ahead with this idea?
"It's a good chance for Trump to try to unite the country," Udall said.
The senator appealed to the President's history of deal-making.
"He's got a book that's widely acclaimed in terms of 'The Art of the Deal.' This is a deal that makes sense for the country," Udall said. "It's a deal that heals the real deep wounds we've had in this election."
There are three justices over the age of 78 who Udall mentioned as possibilities for retirement: Stephen Breyer, Anthony Kennedy and Ruth Bader Ginsburg. But the senator said he hasn't spoken to any of them about his plan.
When asked whether his pitch was realistic, Udall said: "It's just an idea. I threw it out to them. I throw it out to you."
He added that he hasn't ruled out Gorsuch and he remains open-minded about the nominee.
Republicans need eight Democrats to cross over and vote for Gorsuch in order to avoid a Democratic filibuster. Republicans can get around that rule by invoking the so-called "nuclear option," requiring only a majority to move ahead with voting for the nominee. Udall said he doesn't support changing any Senate rules.