(CNN) A day after Bill Taylor, the top US diplomat in Ukraine, undermined President Donald Trump's defenses with his testimony in the House impeachment investigation, most Republicans in Congress blasted not Trump for his conduct but the Democrats for theirs.

In fact, the most significant criticism of the situation by any leading Republican came from Sen. John Thune of South Dakota, who simply acknowledged he was troubled by what Taylor revealed.

"The picture coming out of it, based on the reporting that we've seen, I would say is not a good one," said the second-ranking senator in GOP leadership, in the most significant criticism of the situation by any leading Republican.

But even those comments were the exception among GOP members of Congress.

About two dozen far-right Republican congressmen held a news conference on Wednesday in the basement of the Capitol protesting the impeachment investigation and how it was being handled. They then stormed the secure facility where another witness was set to testify, disrupting the proceedings.

"We're going to try and figure out what's going on behalf of the millions of Americans that we represent that want us to see this Congress working for them — and not obsessed with attacking a President who we believe has not done anything to deserve impeachment," said Rep. Matt Gaetz, a Republican of Florida.

Most Republicans have sided with the President during the impeachment probe, focused less on what he did but how the Democrats are considering the allegations first brought forward by a government whistleblower , who claimed that Trump abused his power, using his public office for personal gain, in asking the President of Ukraine to investigate a potential political opponent. The inquiry, led by House Intelligence Committee Chairman Adam Schiff, has interviewed witnesses in private and limited access to the testimonies to only members who serve on three House committees: Intelligence, Oversight and Foreign Affairs.

"I don't really mind an inquiry," said Rep. Mike Simpson, an Idaho Republican. "I don't like a secret inquiry."

"It's all just a bunch of bulls---," he added.

Some Republicans have expressed concerns by the allegations of Trump's conduct, including the startling conduct described by Taylor . He testified that he had been told by Gordon Sondland , the US ambassador to the European Union, that "everything" Ukrainian President Volodymyr Zelensky wanted, including a White House meeting and military aid to the country, would be held up until he publicly declared investigations sought by Trump.

One investigation concerned alleged Ukrainian interference in the 2016 election, which involves an unsubstantiated theory that that country was behind the hacking of the Democratic National Committee. The US intelligence community and a special counsel investigation have determined that Russia hacked and disseminated materials in order to benefit Trump in his campaign against former Secretary of State Hillary Clinton.

The other would've targeted former Vice President Joe Biden and his son Hunter, who sat on the board of an energy company, Burisma Holdings, whose owner had been probed by the former Ukrainian general prosecutor. There is no evidence of wrongdoing by either Joe or Hunter Biden.

Like Thune, Republican Rep. Paul Mitchell of Michigan, called Taylor's testimony "troubling." GOP Sen. Susan Collins of Maine said it was an "important piece of evidence."

But even these Republicans are critical about the process of the probe.

The same morning as his Republican colleagues rallied to the doors of the impeachment investigation, Mitchell took a different route, reaching out to an unidentified member of the Democratic leadership to try and get more information about what has worried him. The effort was wasted.

"I'll defend and protect the Constitution — that's my oath," Mitchell said. "Not to a party, not to a person."

"But I also won't participate in a political hack job just because someone sees the opportunity to do it," he added.

In the Senate, some Republicans said they weren't able to read Taylor's testimony, hadn't read his now-public opening statement or would be jurors in an impeachment trial and shouldn't weigh in so soon.

"I didn't see it," said Sen. Jim Risch of Idaho. "I didn't hear it. I'm not going to take a third party description of it."

Democrats said that the House impeachment inquiry will get the facts despite the Republican efforts to block witnesses from testifying.

"These witnesses have defied the White House efforts to prevent their testimony by following the lawful requirements of subpoenas," Schiff said. "The President has urged his acolytes in Congress to use other means to try to prevent their testimony, but they won't be successful."

"The American people want to hear the facts — and they will," Schiff added.

In evaluating the information already made public, Democrats have argued that Trump has committed impeachable offenses. Republicans retort that that is ridiculous, since the military aid eventually went through to Ukraine.

"Name me one thing that Ukraine did to release the money," said House Republican leader Kevin McCarthy. "Nothing. To have a quid pro quo you have to exchange on both sides."