Washington (CNN) Some of the White House's most senior foreign policy officials were trying to raise the alarm about the administration's potentially illegal activity in Ukraine well before President Donald Trump's now notorious call with his counterpart in Kiev, according to stunning new testimony in the impeachment inquiry.

The detail suggests that senior figures inside Trump's White House were deeply concerned that the activities by the President and those close to him could reach the level of illegal behavior -- a potentially significant turn in the three-week-old impeachment inquiry by House Democrats.

While it remains unclear whether Trump or his lawyer Rudy Giuliani did actually break the law in going around official channels to deal with Ukraine, much of the conduct now emerging at least appears unethical, off-the-books of regular diplomatic activity and more expansive than it initially appeared.

On Tuesday, Giuliani's lawyer informed Congress the former New York City mayor will defy House Democrats' impeachment subpoena. The Office of Management and Budget also does not plan to turn over the documents that impeachment committees subpoenaed, a spokeswoman said.

The new testimony could seriously challenge White House arguments that Trump did not abuse his power by asking a foreign leader for dirt on a domestic political foe: Joe Biden

It adds to a growing tapestry of evidence that suggests that the call between the US and Ukrainian Presidents and a whistleblower account of behind-the-scenes activity in the White House represents just the tip of the iceberg of what may have been going on.

According to sources familiar with the testimony, Hill quoted Bolton as saying that Trump's lawyer, who was freelancing on Ukraine policy apparently at the President's request, was a "hand grenade" who was "going to blow everybody up."

Bolton is now almost certain to be called as a witness -- a dangerous prospect for a President who ousted him after disagreements over North Korea and Russia policy. According to the sources familiar with Hill's testimony, she also said Bolton warned her that he would not get caught up in what he referred to as a "drug deal" being cooked up on Ukraine by US Ambassador to the European Union Gordon Sondland and White House acting chief of staff Mick Mulvaney.

Hill also testified that the public discord over issues like Ukraine sowed confusion about American policy and was the kind of corruption that the Russians could exploit, according to another source with knowledge of the testimony.

Hill said "corruption is how Putin accesses our system," the source said, although the source did not specify to what exactly Hill was referring. Hill is a former intelligence official and Russia scholar who specializes in the Russian President.

Danger sign for the White House

The testimony of Hill, formerly senior director for Russian and European Affairs on the National Security Council, may also be a sign that the White House will not succeed in its effort to prevent all former officials from testifying as part of a strategy of blanket non-cooperation with the inquiry.

In a letter to the White House counsel's office, Hill's lawyer rejected the idea that much of her testimony would be subject to executive privilege since many details of the affair were now public -- including Trump's call with Ukrainian President Volodymyr Zelensky on July 25 -- a rough transcript of which was released by the White House itself.

And in an eye-opening warning, the lawyer, Lee Wolosky, cited precedent to the effect that privilege disappears if "government misconduct occurred," in an apparent suggestion of possible criminal activity within the White House.

One source told CNN that Hill, a Trump appointee, saw "wrongdoing" in the White House approach to Ukraine and tried to report it to officials.

Hill was concerned that Giuliani was circumventing the State Department to run what some Democrats have labeled a "shadow foreign policy" by seeking the removal of US Ambassador to Ukraine Marie Yovanovitch and pushing for Ukraine to open an investigation into the former vice president and his son Hunter Biden. There is no evidence of wrongdoing in Ukraine by either Biden.

What makes Hill's testimony especially interesting is the fact that she was not on Trump's call with Zelensky on July 25. She had officially left her post by then. That means that her account relates to the period before the telephone call -- suggesting that the scheme to pressure Ukraine was much longer in the making than it first appeared.

Trump insists that the call was "perfect." But the transcript does show the President asking Zelensky for a "favor" when the Ukrainian talks about future defense purchases.

The US President insists there was no "quid pro quo" in his dealings with Ukraine -- a statement apparently called into question by previously released text messages between senior US officials working on the Ukraine issue.

Trump and Republicans attack process

Trump on Monday sought to downplay Hill's evidence.

"Democrats are allowing no transparency at the Witch Hunt hearings. If Republicans ever did this they would be excoriated by the Fake News. Let the facts come out from the charade of people, most of whom I do not know, they are interviewing for 9 hours each, not selective leaks," Trump tweeted.

Republicans, who are angry that Democrats have yet to allow a full floor vote on initiating impeachment procedures, picked up the President's complaint, arguing that tidbits of testimony were being leaked by Democrats for their own political advantage.

"The American people should be able to watch this, and most members of Congress have no idea what's going on in there," Michael McCaul, the top Republican on the House Foreign Relations Committee said on Tuesday.

McCaul said Dems are releasing "little portions that benefit their case. That's not how a prosecutor works, that's not how a case works."

There is no constitutional requirement for Democrats to hold open hearings or to kick off the process before a full House vote. But such a process was followed with the two previous presidential impeachment dramas involving Presidents Bill Clinton and Richard Nixon. There is a growing debate over whether Democrats have an obligation to the American people to hold open, televised hearings and whether having witnesses like Hill testify in public would actually bolster their case against the President.

Hill's evidence thickens the storylines around impeachment at the start of a week of dramatic testimony by other important figures in the administration's foreign policy operation. U S Deputy Assistant Secretary of State for European and Eurasian Affairs George Kent was testifying Tuesday morning in a closed-doors deposition hearing. Kent was among the career officials who sought to shield former Yovanovitch from the campaign of false allegations against her in March 2019, according to internal emails turned over to Congress by State Department Inspector General Steve Linick in early October. Yovanovitch, who was removed from her post in May, testified to the House committees on Friday.

Those emails show Kent, along with acting-Assistant Secretary for European and Eurasian Affairs Phil Reeker, working to provide department counselor Ulrich Brechbuhl and Undersecretary for Political Affairs David Hale with facts to counter the conspiratorial narratives being pushed about the career diplomat.

Sondland, who was earlier prevented by the administration from testifying about the Ukraine scandal is expected to give a deposition, under subpoena, on Thursday.