South Dakota Gov. Kristi L. Noem and Rep. Alexandria Ocasio-Cortez of New York live more than 1,500 miles apart and inhabit entirely different political orbits, but they share a similar space in the minds of ideological warriors who want to upend a pair of titans in the Senate.

The unconfirmed rumor that Congress Member Alexandria Ocasio-Cortez has been thinking about running against NY State Senator, Chuck Schumer, has been circulating for quite some time, but according to the NY Post, New York State Democratic part head, Jay Jacobs is warning AOC not to take on Schumer. Just a few weeks after a group of young climate activists, accompanied by Alexandria Ocasio-Cortez, orchestrated a highly publicized sit-in in House Speaker Nancy Pelosi’s office in.

Conservative and liberal activists are pushing Noem (R), 49, and Ocasio-Cortez (D), 31, to challenge, respectively, Sens. John Thune (R) and Charles E. Schumer (D) in their state’s 2022 primaries.

How Thune, the No. 2 Republican in leadership, and Schumer, the Democratic leader, respond to their standing as high-profile primary targets could reveal a lot about the state of their political parties and whether there is any hope for bipartisan compromise in the Senate.

Of the 34 Senate seats up for grabs in two years, just three incumbents hail from states that voted for a president of the opposing party, including Sen. Kelly Loeffler (R), who first has to win Tuesday’s runoff election in Georgia to be on the ballot again in two years. That means the most competitive portion of the lion’s share of these races could come in primaries.

Liberals have had recent success with primary challenges in House races but have struggled to match it statewide in Senate races, which has had some pining for Ocasio-Cortez to challenge Schumer since her upset victory in the 2018 primary.

Republicans could be in for a replay of the brutal primaries they faced in the Senate in 2010 and 2012, particularly as President Trump heads for the exits with vows to promote primary challenges to GOP incumbents.

In particular, Trump has turned Wednesday’s protest votes in the House and Senate over the final certification of President-elect Joe Biden’s victory into something of a loyalty test. And Thune, usually mild-mannered, has emerged as the most outspoken critic of Trump’s congressional allies for forcing votes on what is normally a perfunctory reading of the actual electoral college results.

“The thing they’ve got to remember is, it’s just not going anywhere. It’s going down like a shot dog,” Thune told reporters Dec. 21, a comment that went viral and prompted Trump the very next day to promote a primary challenge to the incumbent.

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Despite Noem’s public declaration that she will run for reelection as governor, Trump used a New Year’s Day tweet to formally kick off the Noem speculation.

“I hope to see the great Governor of South Dakota @KristiNoem, run against RINO @SenJohnThune, in the upcoming 2022 Primary. She would do a fantastic job in the U.S. Senate, but if not Kristi, others are already lining up,” Trump tweeted.

There’s little love lost among the Hill’s top leaders. Can Biden get them to work together?

Thune and Schumer have taken different approaches to their internal party critics, with the Republican mocking the outgoing president.

“Finally, an attack tweet! What took him so long? It’s fine, that’s the way he communicates,” Thune told reporters in the Capitol on Friday.

He said he has made no effort to patch things up with Trump. “I’m not sure that anything changes his mind once he makes it up,” he said.

Schumer has not publicly poked at liberals, who have long thought the Brooklynite was too close to Wall Street. “Look, throughout my career, I do the job for my constituents and for my country and it always works out,” Schumer recently told Politico, a refrain he uses whenever his own 2022 race is mentioned.

He has taken several not-so-subtle steps to try to neutralize his critics and his potential opponents. The day after the death of Supreme Court Justice Ruth Bader Ginsburg, Schumer appeared with Ocasio-Cortez at a Sept. 19 news conference.

On Dec. 7 he held a Manhattan news conference to announce his support for a top liberal cause, canceling college loan debt. And he appeared there with three incoming House members who won their primaries with anti-establishment support, including Jamaal Bowman (D), who defeated Schumer’s friend, 32-year incumbent Eliot L. Engel, in the primary.

And on Dec. 22, after Trump declared he wanted $2,000 stimulus checks sent to most adults, Schumer jumped on Twitter to throw his support behind Ocasio-Cortez’s legislation calling for just that amount.

Thune and Schumer entered the Senate as giant slayers themselves. In 2004, when South Dakota’s three members of Congress were all Democrats, Thune defeated then-Minority Leader Thomas A. Daschle (D), becoming the first challenger to defeat a party leader in more than 50 years.

By 2010 Thune did not face an opponent in his reelection, and for the past six years the state’s delegation has been entirely Republican. He has more than $13 million sitting in his campaign account.

Schumer defeated a three-term incumbent, Alfonse M. D’Amato, in 1998, knocking off the Banking Committee chairman and claiming a seat Republicans had held for 42 years. New York Democrats have won every Senate race since and lost just one governor’s race — Republican George E. Pataki’s reelection in 2002.

Schumer won his 2016 race with almost 71 percent of the vote, about the same margin as Thune. He has more than $10 million in his campaign account to start the 2022 campaign.

That prowess makes a primary challenge to Thune and Schumer both daunting and attractive, particularly since Democratic primary voters in New York have grown more liberal the same way South Dakota’s GOP voters have grown more conservative.

Noem called Thune “a friend of mine” when she proclaimed she would not challenge him, but that won’t matter to Trump and his closest allies. They will probably spend the next 15 months stoking her as a potential challenger, until the candidate filing deadline in the spring.

And the South Dakota governor is almost unrecognizable to anyone who followed her four terms in the House. She landed in the Capitol in 2011 with a tea party following and a national media that was ready to anoint her the next Sarah Palin, a young conservative woman.

Instead, Noem recoiled from the spotlight and spent eight years maintaining a low profile, a very reliable vote for establishment-friendly GOP speakers.

Most interpreted her 2018 run for governor as an attempt to get further away from national attention, but this year, after some Trump advisers grew close to her, she embraced the president’s anti-mask approach to battling the pandemic even as her state’s death toll soared. She’s now a regular on cable news shows and travels the nation to campaign for other Republicans, and if Trump doesn’t run for president in 2024, some view Noem as a potential top-tier candidate for the GOP nomination.

Ocasio-Cortez took the opposite approach to Noem upon arriving in the Capitol two years ago, embracing the limelight and immediately becoming an ideological flamethrower.

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And she has declared that it’s time to replace Schumer and House Speaker Nancy Pelosi (D-Calif.). “I do think that we need new leadership in the Democratic Party,” she told the Intercept in a December interview.

For now, Schumer will continue with his aggressive approach to hitting all 62 counties in New York, reminding them of how much largesse he brings home.

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And Thune will hope that once Trump is no longer president his tweets will fade from relevance. Back in June, after Trump stoked racial division during protests, Thune told reporters that the president has “his moments” of presidential behavior.

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“As you know, it lasts generally as long as the next tweet,” he added.

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© Jabin Botsford/The Washington Post President Trump, flanked by Florida Gov.-elect Ron DeSantis and South Dakota Gov.-elect Kristi Noem, speaks during a meeting at the White House on Dec. 13, 2018.