A top Democrat on the House Oversight Committee told "Fox News Sunday" that she believes the panel's chairman, Rep. Elijah Cummings, will "end up referring" former Trump attorney Michael Cohen to the Department of Justice for a perjury investigation, after numerous contradictions and inconsistencies have surfaced in his dramatic public testimony late last month.

Rep. Katie Hill, D-Calif., who also serves as the liason to the Democratic leadership, additionally charged that the Democratic National Committee (DNC) erred by blocking Fox News from hosting any Democratic primary debates, saying the move doesn't do anything to "help" the growing partisan tensions.

Hill's comments came as Cohen's own lawyer, Lanny Davis, has sought to clarify Cohen's statements before the House oversight panel, even as Davis insists Cohen tesified truthfully. Several Republicans have accused Cohen of perjury on a variety of matters, and on Thursday, House Oversight Committee Republicans referred Cohen to the DOJ for alleged perjury.

But a perjury referral by Democrats, who control the committee, would mark a major escalation for Cohen's potential legal jeopardy. Fox News exclusively reported on Friday, citing two sources familiar with the matter, that Cohen met with staff for Adam Schiff, D-Calif., for more than 10 hours before his testimony. In addition to his public remarks, Cohen has met with the House panel several times behind closed doors.

Even as she seemingly acknowledged that Democrats "can't go anywhere" on impeaching President Trump at the moment, Hill indicated that Cummings had more than enough justification to request another criminal probe into Cohen, who has already pleaded guilty to lying to Congress in 2017 concerning the duration of negotiations to build a Trump Tower in Moscow.

SCHIFF STAFF WENT TO NEW YORK FOUR TIMES TO MEET WITH COHEN FOR MORE THAN 10 HOURS -- FOR TESTIMONY LASTING ONLY 7 HOURS, SOURCES SAY. WAS HE COACHED?

"I don’t know if he lied or not," Hill said. "I think that this is, Chairman Cummings is incredibly deliberate. I know that he's reviewing the entire testimony, all the transcripts with [GOP ranking member Rep. Jim Jordan] who also is going to make sure that we get to the bottom of this."

Among the key areas of focus: Cohen's own attorney, Lanny Davis, seemingly contradicted Cohen's claims under oath that he had never sought a pardon from the White House.

On Friday, President Trump blasted Cohen, confirming that he denied Cohen's request for a pardon.

"Bad lawyer and fraudster Michael Cohen said under sworn testimony that he never asked for a Pardon. His lawyers totally contradicted him. He lied! Additionally, he directly asked me for a pardon. I said NO. He lied again! He also badly wanted to work at the White House. He lied!" Trump tweeted.

Hill told Wallace she was not sure "how that went down exactly," but suggested that Cohen was in a "panic."

"I would imagine that in the panic that was going on when you’re about to go down [on criminal charges], right, that you’re going to say like 'yeah, figure out whatever you can do,'" Hill said. "And I imagine that Chairman Cummings will end up referring him. That’s just my guess."

Cummings said on Thursday that he has "to make sure" that Cohen's statements were "true inconsistencies and not outright lies,” and claimed he told Cohen personally that he would “nail you to the cross” if he had lied to Congress again. “And I meant that,” Cummings said.

Referencing those comments, Hill told Wallace: "When [Cummings] says something like, 'I'm going to nail you to the cross' he means it. I've seen him in action. He's not going to let this go."

"He's not going to let this go." — Rep. Katie Hill, on Elijah Cummings

And Cohen has also faced scrutiny from multiple fronts -- including CNN and the Trump administration -- for claiming under oath that he had not sought out a job in the Trump White House. Davis later acknowledged that Cohen was, in fact, at one time considering the possibility of working in the White House.

Cohen is set to head to prison in May, although his sentence is yet to be determined. Some Republicans accused Cohen of seeking to garner favor with prosecutors with his testimony.

Still, despite the debate over Cohen's truthfulness, Hill said, the Trump administration is still blameworthy -- even if it may lack criminal culpability.

"I really think that this is about getting to the truth, about showing it to the American people, and then we go from there. But at the end of the day if -- if people -- you know, the citizens of the United States -- don't believe that it has risen to that level, then we can't go anywhere," Hill said. "So really it's about exposing the truth and it's about getting to the bottom of this and it's about asking the questions of 'Is this the kind of government, is this the kind of leadership that we want to see, is this OK, is this the kind of state that we want to leave our democracy in to our children?' And right now I just don't believe that it is."

Hill went on to imply that the media climate has become "more and more partisan," after anchor Chris Wallace pressed for her response to DNC Chairman Tom Perez's decision to ban Fox News from hosting Democratic primary debates. Perez claimed Fox News would not be “fair and neutral” forums for the candidates, citing contested allegations in a recent article in The New Yorker.

"I think it’s the Democratic primary and I think we know that there are basically no Democrats who watch Fox News, so to me that's pretty fair," Hill began, although she later acknowledged that "certainly Independents" would be potential debate viewers.

"I'm here because I do represent a purple district," Hill told Wallace. "You know, I think that there's a lack of bias and I'm hoping that we can change that. I feel like you're treating me without bias, and I appreciate that. And I think that this is something we have to change. I personally don't think it helps when we're saying we're not going to have any of the debates on Fox News."

Hill added: "I don't know how much of that was driven by the candidates, how much of it was driven by the party. I'd like to see all of that change. I want to see the media become as unbiased as possible, but you know, I don't know that we're in that state right now, which is really unfortunate."

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Former DNC Chairman Ed Rendell told Fox News on Thursday that the decision was a grave strategic mistake by Democrats.

“If we could pick the commentators and moderators, I think we should have the debate on Fox, because let me tell you — even if we can persuade 3 percent of Fox viewers, 3 percent last time out, carries Michigan,” Rendell, who served as DNC chair during the 2000 election, said in an interview. “I was the DNC chair, I would say, ‘Give me Bret Baier, Chris Wallace and Juan Williams, and you can have that Fox debate anywhere, anytime, any number of times."

Fox News' Chris Wallace and Brooke Singman contributed to this report.