New Jersey Rep. Jeff Van Drew, another freshman in a pro-Trump district, said he plans to vote no.
The White House quickly criticized the resolution, saying it confirms that the inquiry is a "scam".
The resolution will outline the steps needed to take toward impeachment - including open hearings, the disclosure of transcripts and due process rights given to the President.
"That is why this is now called the Impeachment Hoax!"
Democrats and Republicans got into a shouting match behind closed doors on Tuesday while interviewing a witness in the impeachment investigation, with Democrats accusing Republicans of trying to out the anonymous whistleblower who sparked the impeachment inquiry, according to five sources from both parties. House Speaker Nancy Pelosi has argued that the vote is not being taken to formally authorize the impeachment inquiry, as Republicans have demanded, but will help "to eliminate any doubt as to whether the Trump administration may withhold documents, prevent witness testimony, disregard duly authorized subpoenas, or continue obstructing the House of Representatives".
Schiff heads the House Intelligence Committee, one of three panels leading an impeachment probe against Trump.
Two current National Security Council staff members, Alexander Vindman and Tim Morrison, are scheduled to appear this week and would be the first White House employees to testify in the inquiry.
The House Democratic resolution released Tuesday sets out parameters for their inquiry going forward.
William Taylor, the current top diplomat in Ukraine, testified last week that he was told aid to the country would be withheld until it conducted investigations into Trump's potential 2020 Democratic rival Joe Biden and his family, and into Ukraine's involvement in the 2016 U.S. presidential election.
Jordan, who witnessed Vindman's deposition, said he could not go into explicit detail about the questions Schiff blocked.
The resolution says that the House Intelligence Committee will write a report "setting forth its findings and any recommendations" and that the report will be transmitted to the Judiciary Committee and be made public.
The resolution also states that the minority may request witnesses to be called and issue subpoenas - but those subpoenas can only be issued "with the concurrence of the chair", meaning that Democrats would have to sign off on any Republican-led subpoenas. Even then, the White House's rights remain undefined, unclear, and uncertain - because those rules still haven't been written.
Senate Democrats said Monday they intend to force a floor vote this week to clamp down on the Trump administration's efforts to give states an avenue to bypass certain requirements created by Obamacare.
"We always tell potential whistleblowers that choosing to blow the whistle is a family decision, because it will upend their professional lives", said Irvin McCullough, a national-security analyst at the whistleblower protection group Government Accountability Project.
A federal judge late last week determined that the House inquiries have legal standing as an impeachment investigation.