erick4x4/iStock(WASHINGTON) -- The House of Representatives is expected to vote on Thursday on a resolution laying out the next steps in the impeachment process, according to a senior Democratic aide, after weeks of criticism from Republicans and President Donald Trump that the inquiry was unfair, illegitimate and being conducted in secret

In a letter to colleagues, House Speaker Nancy Pelosi said the resolution "establishes the procedure for hearings that are open to the American people, authorizes the disclosure of deposition transcripts, outlines procedures to transfer evidence to the Judiciary Committee as it considers potential articles of impeachment, and sets forth due process rights for the President and his Counsel."

The vote on this resolution comes as Republicans and the White House have argued against Democrats' handling of the impeachment process, although it's unlikely the resolution will go far enough to satisfy Republicans' demands.

"Speaker Pelosi is finally admitting what the rest of America already knew – that Democrats were conducting an unauthorized impeachment proceeding, refusing to give the President due process, and their secret, shady, closed door depositions are completely and irreversibly illegitimate," White House press secretary Stephanie Grisham said in a statement. Grisham noted she would not be able to comment fully until she sees the full text of the resolution.

The resolution will by introduced by House Rules Committee Chairman Jim McGovern, who tweeted it will "ensure transparency and provide a clear path forward."

Republicans have slammed what they say is a lack of transparency in the impeachment process, as Democrats have called nearly a dozen officials to give depositions behind closed doors. Republicans have called for transcripts of that testimony to be made public, have accused Democrats of cherry-picking information to be released or leaked, and have argued President Trump deserves to have counsel present to cross-examine witnesses.

For some Senate Republicans, the vote is too little, too late.

"They've made up their mind. Their judicial philosophy is guilty. They're going to give the president a fair and impartial firing squad,” said Sen. John Kennedy, R-La.

“A vote now is a bit like un-ringing a bell as House Democrats have selectively leaked information in order to damage President Trump for weeks,” said Sen. Lindsey Graham, R.-S.C. Last week, Graham introduced a resolution calling for the House to hold a vote to initiate a formal impeachment inquiry, to allow Trump to call witnesses on his behalf and to confront his accusers and to give subpoena power to House Republicans.

Graham took some credit for the Democrats' decision to hold a vote, saying in a statement, "There is no doubt in my mind that the overwhelming response House Democrats heard from the American people and Senate Republicans in support of my resolution forced their hand. Today’s announcement is an acknowledgement of the success of our efforts last week.”

Sen. Roy Blunt, a Missouri Republican, is taking a wait-and-see approach.

"Let’s see what it looks like. But if it’s a vote that says that now we’re just formally going to continue to do things exactly the way we’ve been doing them, that wouldn’t be enough to alleviate my concerns. Maybe it will be better than that," Blunt said.

Democrats, led by House Intelligence Committee Chairman Adam Schiff, have promised to make their inquiry public once they are finished gathering information in the classified setting.

Two weeks ago, Pelosi considered holding a vote to formally declare an impeachment inquiry, but ultimately held off.

"The timeline will depend on the truth-line," Pelosi said.

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