(CNN) Michigan Republican Rep. Justin Amash is holding firm on his assessment that President Donald Trump has engaged in impeachable conduct, pushing back on critics Monday afternoon with a fresh round of tweets and comments amid a wave of denunciations from other Republicans -- and a primary challenge.

"People are free to make up their minds about things and make their own opinions," he said of his Republican critics.

Amash initially tweeted his thoughts on obstruction of justice over the weekend after he finished reading the Mueller report, writing that he also believes Attorney General William Barr intentionally misrepresented special counsel Robert Mueller's findings

Amash doubled down on his stance Monday afternoon in another tweet thread , pushing back on arguments that an underlying crime would be necessary to impeach Trump for obstruction. But he hasn't signed on to any impeachment resolutions yet.

"It's a process. It's not like the resolution is just brought up overnight; it's a process," he told reporters Monday. "And you have to come to the right conclusions on how to draft something."

The weekend tweets prompted Jim Lower, a Michigan state representative who once supported Amash, to announce earlier Monday that he would run in next year's Republican primary.

Amash brushed off Lower's candidacy on Monday night, telling reporters that "it's not serious."

"I feel very confident in my district," he said. He also declined to rule out a potential 2020 presidential run.

Lower told reporters he had been planning to announce his candidacy in July, but moved up the announcement after Amash's comments. Lower says he used to support Amash, but his support has faded in the Trump era.

"I helped with his campaign," Lower told the Daily News, a Michigan newspaper. "Hell, I voted for Amash in '10, '12 and '14."

"At the time, I believed in what he was doing, but now I don't," he said. "I've just been very disenchanted."

But Amash's remarks were not a surprise to anyone who follows him closely.

He was the first Republican to express support for an independent investigation into the 2016 election and Russian interference. He was the first Republican to say in 2017 that it could be an impeachable offense if Trump obstructed justice in firing former FBI Director James Comey. And more recently, he drew attention by being the only Republican to ask serious questions designed to uncover potential wrongdoing during a February hearing with Trump's former personal attorney Michael Cohen.

Amash is now the first Republican to argue Trump committed impeachable offenses. His stance set off a flood of headlines and an insult-laden response from the President.

On his way to a rally in Pennsylvania on Monday evening, Trump said Amash has "been against Trump from the beginning" and he added that the Michigan congressman has "been a loser for a long time."

"Personally," said the President, "I think he's not much."

The congressman has also drawn condemnations from Republican National Committee Chairwoman Ronna McDaniel — "The only people still fixated on the Russia collusion hoax are political foes of President Trump hoping to defeat him in 2020 by any desperate means possible," she said — and House Minority Leader Kevin McCarthy, who argued Amash was simply seeking attention.

"It's a question whether he's even in our Republican conference as a whole. What he wants is attention in this process," McCarthy said on Fox News. "He never supported the president, and I think he's just looking for attention."

Amash and his staff have thus far resisted a flood of media interview requests since his remarks over the weekend.

The question now is what Amash will do next.

He has never been a traditional ladder-climbing party loyalist. He is accustomed to being isolated from the vast majority of his peers in Congress, and is often the sole Republican "no" on otherwise party-line votes . He has regularly clashed with party leaders, in the past unabashedly criticizing former speakers John Boehner and Paul Ryan. And his firm libertarian beliefs on issues like surveillance and foreign policy, as well as his focus on pursuing an increasingly distant regular order legislative process, have always set him apart from the GOP.

His decision to share his thoughts on impeachment publicly — something even many Democrats are afraid to do — only cements the divide between him and the group of hardline conservatives he helped found, the House Freedom Caucus, under the Trump presidency.

Amash has headed off establishment-led efforts to unseat him in the past, but this primary is different. It would almost be a test to see if Republicans can truly be independent from Trump and still be successful in the current political environment. During Trump's first two years in office, Republicans in Congress have coalesced behind the President as his high profile critics, such as now-retired Sens. Jeff Flake and Bob Corker, have diminished.

In 2018, Amash won reelection with 54.4% of the vote, after breezing through the GOP primary unopposed. It's clear his race in 2020, if he chooses to run again, won't be so straightforward.

If there's anything of consequence to keep an eye on after Amash's remarks over the weekend, it's whether Amash, as a high-profile libertarian who commands a cult following nationwide, might decide to launch a challenge to Trump in 2020, rather than running again for his seat.

Amash established an independent brand from the beginning of his political career. He has long considered running for president as a third party candidate or breaking off from the Republican Party entirely.

"I would never rule anything out," he told CNN's Jake Tapper in March when asked about running for president in 2020. "That's not on my radar right now, but I think that it is important that we have someone in there who is presenting a vision for America that is different from what these two parties are presenting."

In the already crowded 2020 field, an independent candidate with a preexisting base of support among conservative voters could complicate Trump's path to victory.

"I never stop thinking about these sorts of things," Amash told CNN in a follow-up interview . "It's not because I have any immediate plans or anything like that, but I never stop thinking about those things because there is a big problem with the current two-party system we have, and someone has to shake it up."

"Now, is it possible for anyone to shake it up and make a difference?" he added. "I don't know."