"This resolution does nothing to change the fundamental fact that House Democrats refuse to provide basic due process rights to the administration," the statement said on Tuesday.
Grisham added the resolution, which has been released on Tuesday, confirms that the impeachment inquiry has been "illegitimate" since the beginning because it lacks a proper authorisation vote.
The resolution authorises several congressional committees to complete their investigations in order to determine whether the House of Representatives has sufficient basis to exercise its constitutional power to impeach Trump.
The resolution also provides a list of lawmakers who may question witnesses during the impeachment hearings.
The vote on the resolution is expected to take place on Thursday, according to reports.
On 24 September, House Democrats launched an impeachment inquiry over a whistleblower complaint that claimed Trump might have abused his power by allegedly pressuring Ukrainian President Volodymyr Zelenskyy during 25 July phone call to investigate potential corruption by former Vice President Joe Biden and his son Hunter.
Trump released the transcript of the call and characterised the impeachment inquiry as another political witch hunt aimed at reversing the result of the 2016 US presidential election.