Rep. Justin Amash Justin AmashInternal Democratic poll shows tight race in contest to replace Amash Centrist Democrats 'strongly considering' discharge petition on GOP PPP bill On The Trail: How Nancy Pelosi could improbably become president MORE (R-Mich.) on Tuesday said he would not rule out a third-party challenge to President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE in 2020.

The Hill asked Amash if he is thinking about leaving the Republican Party to run for president as the Libertarian Party candidate.

“I’m just focused on defending the Constitution, it’s not something I’ve thought about,” Amash said. “I don’t take things off the table like that, but it’s not something at the forefront of my considerations right now. I’m just focused on my job. I wouldn’t take running for governor off the table or Senate or statehouse, I don’t take things off the table.”

Amash this week became the first Republican in the House to support impeachment proceedings against Trump.

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In interviews this year, Amash has toyed with the idea of switching parties and running for president. The Michigan Republican has described himself as the only Libertarian member of Congress and has been increasingly critical of the GOP, accusing the party of abandoning its conservative values in the age of Trump.

Libertarian National Committee Chairman Nicholas Sarwark told The Hill there’s a full-scale effort underway to convince Amash to register as a Libertarian and run for president against Trump.

“There are a lot of Libertarian Party members actively encouraging Rep. Amash to switch parties and seek the Libertarian nomination,” Sarwark said. “This is probably the most organized recruitment effort I’ve seen going back to 2012 when people were trying to recruit [former Texas Rep.] Ron Paul.”

Former New Mexico Gov. Gary Johnson Gary Earl JohnsonWhat the numbers say about Trump's chances at reelection Presidential race tightens in Minnesota as Trump plows resources into state The Hill's Campaign Report: Biden condemns violence, blames Trump for fomenting it l Bitter Mass. primaries reach the end l Super PAC spending set to explode MORE was the Libertarian Party presidential candidate in 2016. Massachusetts Gov. William Weld William (Bill) WeldRalph Gants, chief justice of Massachusetts supreme court, dies at 65 The Hill's Campaign Report: Biden visits Kenosha | Trump's double-voting suggestion draws fire | Facebook clamps down on election ads Biden picks up endorsements from nearly 100 Republicans MORE ran on the ticket as vice president.

There was hope in some quarters that Johnson would meet the polling requirements to make the general election debate stage, but he struggled with embarrassing gaffes and Washington insiders never took his candidacy seriously.

Still, the Johnson-Weld ticket earned 4.5 million votes in the general election, tripling the previous best showing by the Libertarian Party.

There is hunger in some quarters on the right for a conservative challenger to Trump in 2020.

Weld launched a primary challenge earlier this year, but his candidacy has failed to gain traction. Trump maintains about 90 percent support from Republicans, and the national party has taken steps ensure a primary challenger does not pose a threat to the president’s reelection efforts.

The “Never Trump” Republicans, led by former Weekly Standard editor William Kristol, have been trying to recruit their own candidate to either run in the primary or as an independent, with no success.

There has generally not been much overlap between Kristol’s neoconservatism and the libertarian right, but Kristol and his allies have praised Amash for taking a stand on the matter of impeachment.

“I say this as someone at odds with Amash on lots of issues important to me and I think to him — all honor to Justin Amash, who has done so much today to set an example of constitutional responsibility and mature, civic discourse,” Kristol tweeted.

National Review writer David French, whom Kristol tried to recruit to challenge Trump in 2016, said he’d vote for Amash if he is the Libertarian Party nominee in 2020.

While third-party efforts traditionally have fallen into the background of a presidential race, Amash could have an enormous impact on the 2020 general election in his home state of Michigan.

Trump carried Michigan by fewer than 11,000 votes, and the Wolverine State will be a top battleground state for both sides in 2020, along with Wisconsin and Pennsylvania.

Trump’s allies are not taking the threat from Amash seriously at the moment, dismissing chatter about his third-party bid as a total fantasy.

Still, the White House and GOP leaders in Congress are furious with Amash for taking a stance in favor of impeachment.

The president has lashed out at Amash over Twitter, calling him a “total lightweight” and accusing him of grandstanding “for the sake of getting his name out there.”

“Justin is a loser who sadly plays right into our opponents’ hands,” Trump said.

House Minority Leader Kevin McCarthy Kevin Owen McCarthyMcCarthy threatens motion to oust Pelosi if she moves forward with impeachment Kate Schroder in Ohio among Democratic challengers squelching GOP hopes for the House McCarthy's Democratic challenger to launch first TV ad highlighting Air Force service as single mother MORE (R-Calif.) has unloaded on Amash, calling his remarks about impeachment “disturbing” and questioning “whether he’s even in our Republican conference.”

“He never supported the president, and I think he's just looking for attention,” McCarthy said on Fox News’s “Sunday Morning Futures."

McCarthy also accused Amash, who co-sponsored the bill to block Trump’s emergency declaration at the border, of voting more with Speaker Nancy Pelosi Nancy PelosiHoyer: House should vote on COVID-19 aid — with or without a bipartisan deal Ruth Bader Ginsburg lies in repose at Supreme Court McCarthy threatens motion to oust Pelosi if she moves forward with impeachment MORE (D-Calif.) than with Republicans.

“I think everyone knows he’s lying,” Amash fired back. “But that’s typical Kevin."

Updated at 4 p.m.