Updated at 4:55 p.m. to include additional information throughout.

WASHINGTON — With President Donald Trump's anti-Robert Mueller tirades fueling speculation that he might fire the special counsel overseeing the Russia probe, a number of Texas Republicans say they don’t think he would take such drastic action.

But if he does, they say it would be a big mistake.

None so far has echoed warnings that firing Mueller would invite impeachment, but some are making it clear the president would face serious political and potentially legal ramifications.

Texas Sen. John Cornyn, the No. 2 Republican leader, told various news outlets this week it would be a “bad mistake” to fire Mueller, one that could cause “all sorts of unintended consequences. ”

Cornyn said that message has been conveyed to the president, though he added that he doesn’t believe Trump would take such action.

“I really hope he doesn’t do that,” said Rep. Kenny Marchant, R-Coppell. “I want the thing to be completed, I want [Trump] to be exonerated and I want the whole thing to be very clean.”

Dallas Rep. Pete Sessions, chairman of the House Rules Committee, said while he doesn’t believe Trump is seeking to oust Mueller, even Trump “would say that would be a mistake.”

The warnings come as Trump continues his attacks on Mueller, who is 10 months into a criminal probe investigating Russian interference in the 2016 presidential election, links with the Trump campaign and any subsequent obstruction of justice.

Trump has long proclaimed his innocence, but upped his criticism of the probe in recent days on Twitter by invoking Mueller by name, questioning the impartiality of the investigators and declaring the inquiry a “total WITCH HUNT with massive conflicts of interest.” Trump also said the probe should “never have been started.”

“Why does the Mueller team have 13 hardened Democrats, some big Crooked Hillary supporters, and Zero Republicans? Another Dem recently added...does anyone think this is fair? And yet, there is NO COLLUSION!” he tweeted earlier this week.

The Mueller probe should never have been started in that there was no collusion and there was no crime. It was based on fraudulent activities and a Fake Dossier paid for by Crooked Hillary and the DNC, and improperly used in FISA COURT for surveillance of my campaign. WITCH HUNT! — Donald J. Trump (@realDonaldTrump) March 18, 2018

On Wednesday, the president dug in again with a series of typo-laden tweets, quoting comments made on Fox News by Harvard law professor Alan Dershowitz, who said he was opposed to the selection of Mueller and that Trump was right to say that no special counsel should have been appointed.

“Special Council is told to find crimes, whether a crime exists or not. I was opposed to the selection of Mueller to be Special Council. I am still opposed to it. I think President Trump was right when he said there never should have been a Special Council appointed because..... — Donald J. Trump (@realDonaldTrump) March 21, 2018

...there was no probable cause for believing that there was any crime, collusion or otherwise, or obstruction of justice!” So stated by Harvard Law Professor Alan Dershowitz. — Donald J. Trump (@realDonaldTrump) March 21, 2018

It's the latest missive in a tweet storm that began last weekend, after Trump's personal attorney, John Dowd, called for the end of the probe — statements Dowd insisted were on his own behalf after initially claiming that he was speaking for the president.

The issue has become a sideshow on Capitol Hill this week, as lawmakers strive to pass a massive spending bill before government funding expires at the end of Friday.

House Speaker Paul Ryan said Tuesday that he has "received assurances" that Trump will not fire Mueller. Democrats, meanwhile, are planning news conferences to highlight what they call Trump's threats to the "rule of law."

Robert Mueller, the special counsel investigating Russian interference in the 2016 election, has in recent weeks subpoenaed the Trump Organization to turn over documents, including some related to Russia, according to two people briefed on the matter, the New York Times reported on March 15. (Doug Mills / The New York Time)

Impeachment?

A few Democrats have already demanded impeachment over the firing of former FBI director James Comey, as well as for a number of controversial statements he's made, such as his response to racially-fueled violence in Charlottesville, Va., last year.

But Trump’s latest moves have even a few Republicans — though none in the Texas delegation — saying removing Mueller increases the risk.

South Carolina Sen. Lindsey Graham told radio host Hugh Hewitt that firing Mueller would "probably" be an impeachable offense, "if he did it without cause."

Then there’s outgoing Arizona Sen. Jeff Flake, a staunch Trump critic, who implored the president on Tuesday to stay away from firing Mueller because it could “create a constitutional crisis.

"Our only constitutional remedy is after the fact, through impeachment," Flake tweeted. "No one wants that outcome. Mr. President, please don't go there."

We are begging the president not to fire the special counsel. Don't create a constitutional crisis. Congress cannot preempt such a firing. Our only constitutional remedy is after the fact, through impeachment. No one wants that outcome. Mr. President, please don't go there. — Jeff Flake (@JeffFlake) March 20, 2018

Meanwhile, at least one Texas Republican said Mueller deserves to get the boot.

Tyler Rep. Louie Gohmert, at a "Conversations with Conservatives" session with reporters on Wednesday, said “Mueller should be fired” but likely won’t be, because Trump would face so much backlash from "all the establishment Republicans that think they’d have to come after Trump if he were fired.”

A more common stance among Texas Republicans is that Trump should let the investigation play out and leave Mueller alone.

Ennis Rep. Joe Barton said he’d advise Trump to “just do the best job you can as president, and ignore it,” barring legally-required responses.

Rep. John Culberson, a Houston Republican who has been targeted this fall by Democrats hoping to take advantage of anti-Trump sentiment, offered this general advice: “Law enforcement investigations are like Plutonium-238: Don’t go anywhere near them, don’t touch them, don’t look at them. Just stay away.”

'Setting the stage'

Democrats have pounced on Trump’s tweets and his attorney’s call for ending the probe as obstruction in the making.

"I've believed for a while that [Trump] could be setting the stage to arrange for Bob Mueller to be fired," San Antonio Rep. Joaquin Castro, a Democrat and member of the House intelligence panel, told CNN on Monday.

“If you look at what the president has said and tweeted, it’s very clear that he’s become very agitated that the investigation is still open, that it’s getting closer to him, that it’s probably getting closer to his inner circle and that it may bear fruit when it comes to prosecutions of people close to him,” he continued.

McAllen Rep. Vicente Gonzalez called the tweets a clear threat that already have consequences.

“By threatening to fire [Mueller], the president is obstructing the government’s ability to defend American values and American institutions,” he said in a prepared statement.

Houston Rep. Sheila Jackson Lee is among the Democrats who say legislation is needed to protect Mueller. She called on Congress to pass her own measure, known as the “Special Counsel Independence Protection Act,” which has nearly 130 Democratic co-sponsors.

“The firing of former FBI Deputy Director Andrew McCabe is no coincidence, and appears part of a larger pattern to undermine, impede and obstruct the Special Counsel’s investigation into Russian interference,” she said in a prepared statement.

Cornyn has dismissed the need for such legislation, calling it unnecessary because Trump knows that firing Mueller would be a mistake.

On Tuesday, the White House downplayed the president’s attacks on Mueller, saying an ouster is not under consideration. Press secretary Sarah Huckabee Sanders said that firing Mueller would not be the “most productive step forward.”

Still, several prominent Republicans have warned Trump to lay off his Mueller criticisms in recent days. Utah Sen. Orrin Hatch said firing Mueller would be “the stupidest thing" the president could do.

Texas Sen. Ted Cruz, who initially praised Mueller's appointment as special counsel last May but later called it a "partisan fishing exercise," declined to weigh in on the possibility that Trump may try to force out Mueller.

"I have a longstanding rule of thought, which is that I don't comment about tweets, and I won't comment about the random comment of the day," Cruz told The Texas Tribune.

Sign of frustration

As Democrats and a few Republican senators sound the alarm, several Texas Republicans in Congress shrugged off the president’s tweets as a sign of little more than frustration.

“It’s apparent and understandable that the president certainly is not happy about things. ... There’s been no evidence to turn up so far that there’s been Russian collusion,” said Rep. Brian Babin, R-Woodville, referring to the ongoing investigation into potential ties between the Trump campaign and the Kremlin.

But, he added, “He has no intention of firing Mr. Mueller.”

Marchant agreed, saying he didn’t interpret Trump’s statements to mean he is “fixing to fire” Mueller as much as he was agitated by McCabe, whom Trump accused of being a pro-Hillary Clinton partisan.

“McCabe had just been fired, and I think he was just simply reacting to that,” Marchant said.

Washington bureau chief Todd J. Gillman contributed to this report.