Even before Scott Walker dropped out of the race for president, his Republican rivals for the White House were chasing after the remnants of his once high-flying campaign.

Walker's opponents openly gossiped about the Wisconsin governor's political challenges as they gathered in California for last week's presidential debate. Once he formally left the race Monday afternoon, the jockeying only intensified.

As Walker was calling it quits during a news conference at home in Wisconsin, his national finance co-chairman, Anthony Scaramucci, was fielding calls from five campaigns — including from three candidates themselves.

"Out of respect to him, I want to talk to him before I do anything with anyone else," said Scaramucci, who was on deck to host several New York City fundraisers for Walker this week.

By the end of the night, several campaigns had moved from outreach to bragging about who from Walker's team they had won over. Texas Sen. Ted Cruz talked up additions in Iowa, Georgia and Nevada. Former Walker supporters in Iowa and New Hampshire said they were now in for Florida Sen. Marco Rubio.

Former Florida Gov. Jeb Bush called Walker a "great public servant" — and quickly urgedWalker's supporters to consider him. Walker had a large Iowa organization, complete with leaders in each of its 99 counties, and Bush said he and his team were trying to win them over.

"That's been some of the effort this afternoon and going forward," Bush told reporters after a campaign stop in northern Iowa. "We're working them hard for sure."

Warning that the 2016 campaign had become too nasty, Walker said Monday he's "being called to lead by helping to clear the field in this race so that a positive conservative message can rise to the top." While stepping aside, he urged others to quit, too — suggesting that a smaller pool of candidates would be better positioned to take down Republican front-runner Donald Trump.

"I encourage other Republican presidential candidates to consider doing the same, so the voters can focus on a limited number of candidates who can offer a positive conservative alternative to the current front-runner," Walker said.

None are expected to do so anytime soon.

Ohio Gov. John Kasich distributed a fundraising appeal 90 minutes after Walker'sannouncement noting that he's "the only Midwestern governor in the race who can bring our values to Washington, D.C." Former technology executive Carly Fiorina is surging on the back of a strong performance in the second GOP debate.

Some in the party suggested the biggest beneficiary of Walker's exit may be Rubio, who, like Walker, is considered a fresh face with the ability to unify the GOP's divided factions.

Both men are under 50 and hold a "next-generation appeal," said Frank Luntz, a Republican pollster who is unaligned in the race, but offered his California home toWalker for a post-debate fundraiser last week.

"They're both ideological without being uncompromising, and they have both earned their conservative stripes," Luntz said, noting Walker's fight with public-employee unions and Rubio's battle with then-Republican favorite Charlie Crist in the GOP contest for Florida Senate in 2010.

Walker and Rubio also share a personal connection and acknowledged early speculation that they might run on the same ticket.

"It was personally hard, but you know when it's over," said Cliff Hurst, who was Walker'sNew Hampshire co-chairman. Yet he said he had recently turned his attention to Rubio. "I've always been impressed with his character, his intelligence and his knowledge of how it all works," he said.

It may take weeks for a clear picture to emerge of the political landscape withoutWalker. But with several of the more than a dozen candidates still in the race registering in the low single digits in national polls, the competition for Walker's staff and donor network will only intensify in the coming days.

Within minutes of Walker's announcement, the Chicago-based Ricketts family was bombarded with calls from six GOP campaigns, including from some of the candidates themselves, a person close to the family said.

The billionaire family is likely be very active in the primary process as donors to someone else, but they don't immediately know who that person will be, the person said, speaking on condition of anonymity in order to discuss private conversations with the family.

"Our nation's future is at stake," said Todd Ricketts, who served as a national finance co-chairman for Walker. "And while I was proud to help Gov. Walker, I will keep working hard to make our country a better place."

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Associated Press writers Tom Beaumont and Catherine Lucey in Des Moines, Iowa, and Kathleen Ronayne in Concord, New Hampshire, contributed to this report.

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