Facing a Tuesday deadline, Sale sent a two-paragraph letter to the House Intelligence Committee telling the panel that Giuliani would not comply with the subpoena "because this appears to be an unconstitutional, baseless, and illegitimate 'impeachment inquiry.'"

Giuliani also "adopts all the positions" that White House Counsel Pat Cipollone spelled out last week in a separate letter resisting compliance with the House's impeachment subpoenas, Sale added. And he suggested Democrats would need to litigate if they wanted to see Giuliani's documents, explaining that they were all protected by attorney-client, attorney work-product and executive privileges.

Legal experts have cast doubt on Giuliani's claims that he can defy a subpoena from Congress by citing lawyer privileges when he has publicly confirmed his outreach to a variety of people besides his client, as well as his statements that he works for Trump in other capacities besides just being the president's lawyer. But securing those materials won't come without a fight that Democrats may not even need to pursue.

"The trouble is, if you want to get information out of Giuliani you're going to have to get it one axe fight at a time," Frank Bowman, a University of Missouri law professor and impeachment expert, said in a recent interview.

For his part, Giuliani explained to POLITICO on Tuesday that he wasn’t represented by Sale anymore. “Jon has done what I retained him for,” Giuliani wrote.

Federal prosecutors haven’t confirmed a Giuliani-specific investigation, though the U.S. attorney from the Southern District of New York who last week brought criminal charges against two of Giuliani’s associates for alleged campaign finance violations said during a news conference that the Justice Department probe was ongoing.

On Friday, The New York Times reported that Giuliani was under federal investigation tied to his efforts to undermine Marie Yovanovitch, the U.S. ambassador to Ukraine who was recalled this past spring amid a wider campaign to pressure the country’s leaders into investigating Trump’s political opponents.

In a sign that the federal investigation out of New York is widening, a spokesman for former Rep. Pete Sessions confirmed on Tuesday that the Texas Republican got a grand jury subpoena about the Ukraine affair and would be "providing documents to their office related to this matter over the next couple of weeks as requested." According to the Wall Street Journal, which first reported details about the subpoena, federal prosecutors are seeking documents from the ex-congressman related to Giuliani's business dealings with Ukraine and to size up Sessions' knowledge of Giuliani's activities.

Giuliani said over the weekend that he had “no knowledge of any probe” into his dealings in Ukraine and that he continued to serve as a personal attorney for Trump. Another source familiar with the Trump legal team’s arrangements said Giuliani would still work on all impeachment matters but would be restricted from handling anything dealing with Ukraine because he’s also likely to be a witness in the congressional proceedings.

Sources familiar with Giuliani’s situation said he didn’t think he needed to tap a new lawyer for any potential criminal case. But a back-channel effort is nonetheless underway to try to line him up with new counsel. Among the names floated include Marc Mukasey, though the former Giuliani law partner has his own conflict representing the president and his namesake Trump Organization.

Kyle Cheney contributed to this report.