US President Donald Trump meets with Nikki Haley, the United States Ambassador to the United Nations in the Oval office of the White House on October 9, 2018 in Washington, DC. Olivier Douliery | AFP | Getty Images

On the day Nikki Haley resigned as the U.S. ambassador to the United Nations she made it clear she has no intention to run for president in 2020. That's not stopping Republican operative Bill Kristol from approaching her to see whether she would run against President Donald Trump in a primary. "When she leaves the administration I'd be happy to buy her lunch and see what's happening with Trump, the economy, [special counsel] Bob Mueller" and whether she wants to run in 2020, Kristol said in an interview on Thursday. "I'll hope to speak with her as well as many other people." He added: "What we are doing is laying the groundwork and showing there's a path and helping create that path for anyone who chooses to run. That decision is obviously up to them." The reason for his interest in Haley is that she has something none of his other potential candidates have: insight into the inner workings of the administration. The awareness she gained from working directly with the president could give her an advantage in a potential fight versus Trump in a primary, Kristol said. "The advantage she has is that, while she's clearly different from Trump, she's worked with him. She's impressive," he added. Representatives from the U.S. mission to the UN, the White House and Trump campaign did not respond to requests for comment. Tweet:

Kristol targets Trump

Kristol, a strong critic of Trump who served in the administrations of Republican presidents Ronald Reagan and George W. Bush, has put together what he hopes will be a formidable 2020 political juggernaut through his nonprofit, Defending Democracy Together. The goal of the organization is to convince prospective candidates that there's a path to defeating Trump in a primary and that "saving the party, and perhaps the country, is worth the effort," Kristol said. He has previously engaged with other potential GOP primary challengers who also have been critical of the president including Sen. Ben Sasse of Nebraska, outgoing Sen. Jeff Flake of Arizona and Ohio Gov. John Kasich. Other possible nominees on Kristol's radar are Massachusetts Gov. Charlie Baker and Maryland Gov. Larry Hogan. Sasse, Kasich and Hogan haven't ruled out running against Trump in the next election. Flake announced at the Forbes 30 Under 30 that it's unlikely he will challenge the sitting president. "I don't see that happening in my case," he said at the time. Baker hasn't recently commented on making a move for the presidency. Representatives for Sasse, Flake, Kasich, Baker and Hogan did not return requests for comment. Kristol is also readying a super PAC for 2020 GOP candidates that would allow his team to raise unlimited amounts of cash and push out campaign advertisements backing a particular nominee. For now, Kristol and his team are polling voters in swing states such as New Hampshire and Iowa about having a Republican run against Trump in the next election. In a recent poll funded by Kristol's organization, Iowa and New Hampshire voters seem to believe she could be a formidable challenger to Trump. The survey, which focused on likely GOP caucus voters and primary participants, found that 47 percent would consider another option over Trump in 2020. Haley topped the candidate list with 52 percent saying they're open to considering her as an alternative. The poll was conducted by data analytics firm Applecart. The firm's CEO, Matt Kalmans, told CNBC his team conducted approximately 1,200 live calls in each state. Iowa's results had a margin of error of plus or minus 2.81 percent while New Hampshire's had one of plus or minus 2.73 percent. At a recent rally in Murphysboro, Illionois, Trump went on the offensive against Kristol and other conservatives who have opposed his presidency. "The losers that were...some guy named Kristol. Bill Kristol. He called it wrong from Day One," he declared.

Feuds and friends in the White House

Haley is apparently leaving the administration on good terms. She and Trump announced her decision in a joint announcement last month, in which the two exchanged praise. Trump said he would like her to come back to work for his administration one day. Still, she had her share of battles with a few members of Trump's inner circle. One of the public feuds was with National Economic Council Director Larry Kudlow, which came after Haley announced the U.S. would be imposing sanctions on Russia. In April, Kudlow said Haley must have been having "momentary confusion" following the decision. Haley fired back at the time, saying, "With all due respect, I don't get confused." She's also reportedly has a strained relationship with National Security Advisor John Bolton, who's been a longtime critic of the U.N. On the other hand, she surrounded herself with powerful allies in the White House including Trump's son-in-law and senior advisor Jared Kusher and the president's elder daughter, Ivanka Trump, who is Kushner's wife and a fellow White House advisor.

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