New York (CNN Business) Republican Sen. Lindsey Graham, whose stock has risen in conservative circles since he became a close ally of President Trump, has come under fire in recent weeks from right-wing media personalities who do not think he has done enough to probe supposed Democratic corruption.

The right-wing media personalities — including heavyweights such as Tucker Carlson, Lou Dobbs, Rush Limbaugh, and others — have suggested Graham is failing the President by not using his power as the chair of the Senate Judiciary Committee to investigate the origins of the Russia probe and, most recently, the impeachment inquiry

Graham in May promised that the Senate Judiciary Committee — which is responsible for oversight of the Justice Department, including the Federal Bureau of Investigation — would "look long and hard" into how the investigation into the Trump campaign's interactions with Russia during the 2016 presidential election started. He then repeated that it was necessary to probe the origins of the Russia investigation in interviews with the media.

But such hearings have not materialized. In recent weeks, the Ukraine scandal has put conspiracy theories related to the origins of the Russia probe back in the spotlight.

Right-wing media personalities, in addition to Trump himself, have recently resurfaced a debunked conspiracy theory that Ukraine, and not Russia, hacked the Democratic National Committee's emails in 2016. The theory is popular in pro-Trump circles because it lets Russia off the hook for election interference, and suggests Special Counsel Robert Mueller's probe was unnecessary and had corrupt origins.

The Justice Department has opened up a probe into the origins of the Trump-Russia investigation.

But Graham is now facing scrutiny for not delivering on his word.

"Lindsey Graham is the Committee Chairman. He claimed he would get to the bottom of it," Carlson, who hosts a prime time show on Fox, said in an October 21 interview with Republican Sen. Rand Paul. "Why hasn't he?"

Paul agreed that Graham "has the power" to "drag these people in" for questioning, and said he has "encouraged him publicly and privately to do this."

Carlson added later in the segment, "When he goes on cable news, not on this show, but in others, and he makes these claims, 'I'm going to do this. I'm going to do this. I'm going to do that. I'm fighting for you.' And then he doesn't."

Carlson is far from alone. The chorus from the right-wing media has been growing louder over the last several weeks.

"Lindsey Graham, you are the chairman of the Judiciary [Committee] in the Senate," Sebastian Gorka, the former White House aide who now hosts a radio show, said during a November 8 Fox Business Network appearance. "You can subpoena whoever you want. You can subpoena Adam Schiff. You can subpoena the whistleblower. Where are you?"

Rush Limbaugh, the top-rated conservative talk radio host, asked a similar question.

"A lot of people raised a good point, where's Lindsey Grahamnesty? Where is he?" Limbaugh asked during the October 22 episode of his show. "He's got a Senate committee that he runs, Judiciary Committee. He could be subpoenaing people, he could be demanding to see — he could be doing in the Senate what they're doing in the House except he could be doing it to the people that ran this phony investigation into Trump."

And Lou Dobbs, the Fox Business Network host, said in late October that Graham is an "embarrassment" who "has not lifted a finger for the president."

On the pro-Trump internet, The Gateway Pundit — a blog notorious for peddling conspiracy theories but which is popular on the far-right and amongst Trump supporters — has been blasting Graham.

"HE LIED!" one headline recently read. "Fraudster Judiciary Chair Lindsey Graham Has REFUSED to Call any Hearings on FBI, CIA, Spygate, Hunter Biden, Joe Biden, Mueller, Stefan Halper."

Trump is known to consume right-wing media, so the commentary could help shape his opinion of Graham, who has become a close ally of his in the Senate. Carlson, Limbaugh, and Dobbs are all known to be close to Trump, giving their opinions extra weight.

A spokesperson for Graham declined requests for comment on the attacks from right-wing media when reached by CNN Business.

The Graham spokesperson, however, pointed to a recent interview Graham did with Sean Hannity on Fox in which Graham said some areas of jurisdiction fell under other Senate committees.

Trump himself has encouraged Graham to investigate his perceived political enemies.

When asked in October about Graham's criticism of his decision to withdraw from Syria, Trump said Graham "ought to find out what happened" with former FBI Director James Comey, former FBI Deputy Director Andrew McCabe, former FBI agents Lisa Page and Peter Strzok, and former President Barack Obama.

"That's what Lindsey ought to focus on," Trump said, seemingly referring to the origins of the Russia investigation.