President Donald Trump speaks about the shootings in El Paso and Dayton as Vice President Mike Pence looks on in the Diplomatic Room of the White House in Washington, Aug. 5, 2019.
President Donald Trump speaks about the shootings in El Paso and Dayton as Vice President Mike Pence looks on in the Diplomatic Room of the White House in Washington, Aug. 5, 2019.

The case for obstruction by the Trump administration continues to build, House Democrat Adam Schiff says, after senior members and Trump lawyer Rudy Giuliani defied subpoenas in the impeachment inquiry.

Vice President Mike Pence's office called the Democratic-led House inquiry "self-proclaimed" and the subpoena "too broad."

The Pentagon also says it is "unable to comply" at this time for legal reasons.

The White House budget office also rejected the request, and Trump's personal attorney, Rudy Giuliani, also said no to the subpoena for documents related to his efforts to pressure Ukraine to investigate Joe Biden.

"This appears to be an unconstitutional, baseless, and illegitimate impeachment inquiry," Giuliani's lawyer, Jon Sale, said in a letter to the intelligence committee. "The subpoena is overbroad, unduly burdensome, and seeks documents beyond the scope of legitimate inquiry," Sale wrote, adding that the information the Democrats want is protected by attorney-client privilege.

FILE - Rep. Michael McCaul, R-Texas, talks with reporters, Nov. 29, 2016, in New York.

Late Tuesday, Congressman Michael McCaul, the lead Republican on the House Foreign Affairs Committee, said the impeachment inquiry is being conducted "behind closed doors when it should be in front of the American people."

"I call upon the Speaker to put that resolution on the floor so we can move forward in a more transparent way that's more open to the American people because at the end of the day, they are going to be the ones who suffer from an unjust process," McCaul said.

House Intelligence Committee Chairman Adam Schiff, D-Calif., talks to reporters about a transcript of a call between President Donald Trump and Ukrainian President Voldymyr Zelenskiy, at the Capitol in Washington, Sept. 25, 2019.

But Schiff said Republicans are completely represented in the closed-door hearings, saying they are given every opportunity to question witnesses and see evidence.

Those hearings continue Wednesday with testimony from Michael McKinley, a former senior advisor to Secretary of State Mike Pompeo.

The White House has demanded the full House of Representatives vote on whether there should be an inquiry.

Speaker of the House Nancy Pelosi, D-Calif., is surrounded by reporters as she arrives to meet with her caucus at the Capitol in Washington, after declaring she will launch a formal impeachment inquiry against President Donald Trump.

Speaker Nancy Pelosi said late Tuesday nothing requires such a vote and there will not be one at this time. She said the House is honoring its responsibilities and the constitution.

"We're not here to call bluffs. This is not a game for us. This is deadly serious," she said.

Trump's personal attorney Giuliani was deeply involved in pressuring Ukraine to open a corruption probe into Democratic presidential candidate Joe Biden and his son, Hunter Biden.

Democrats investigating Trump, and even some inside the White House, suspect Giuliani is running a shadow foreign policy outside the State Department on Trump's behalf.

Former National Security Advisor John Bolton called Giuliani "a hand grenade who is going to blow up everybody," a former White House aide reportedly told the impeachment inquiry.

Fiona Hill was a White House national security official for Russian and European affairs. She testified behind closed doors Monday.

People familiar with her testimony said she told the lawmakers that Bolton and others in the Trump administration were troubled by Giuliani's efforts toward Ukraine. Bolton reportedly said he was not part of any "drug deal" Giuliani and White House Chief of Staff Nick Mulvaney "are cooking up."

Former National Security Adviser John Bolton gestures while speaking at the Center for Strategic and International Studies in Washington, Sept. 30, 2019.

Bolton has not commented.

The House impeachment inquiry also heard testimony Tuesday from Deputy Assistant Secretary of State George Kent.

Other officials are scheduled to testify this week, including U.S. Ambassador to the European Union and Trump campaign donor Gordon Sondland.

Sondland exchanged a series of text messages with other diplomats who were enlisted to help get Ukraine to investigate Biden.

In one message, Sondland wrote that Trump insists there would be no quid pro quo with Ukraine. He is expected to now testify that Trump himself dictated that message.

U.S. President Donald Trump speaks during a bilateral meeting with Ukraine's President Volodymyr Zelenskiy on the sidelines of the 74th session of the U.N. General Assembly in New York, Sept. 25, 2019.

The Trump-Ukraine scandal was set off when an intelligence whistleblower expressed concern to the inspector general about Trump's July 25 telephone call with Ukrainian President Volodymyr Zelinskiy.

A White House-released transcript of the call shows Trump apparently urging Zelinskiy to open a corruption investigation into the Bidens, including Hunter Biden's job with a Ukrainian energy company.

Trump also alleged that when Joe Biden was U.S. vice president, he threatened to withhold loan guarantees to Ukraine unless an earlier corruption probe into the gas company was stopped.

No evidence of wrongdoing by Joe or Hunter Biden has surfaced. But reaching out to a foreign government to dig up dirt on a rival is considered to be interference in a presidential election and an impeachable offense.

House investigators also want to know if Trump would release $400 million in badly-needed U.S. aid to Ukraine if Ukraine would cooperate in a Biden investigation.

Trump has describes his call with Zelinskiy as "perfect" and accuses the Democratic-led house of a witch-hunt.