CHICAGO (CBS Chicago/CBS News) — Hundreds of people braved frigid temperatures in downtown Chicago Tuesday night to rally in support of impeaching President Donald Trump.

The group gathered in Federal Plaza in spite of frigid temperatures. They then marched north on State Street.

Among the speakers for the event were Cook County Commissioner Brandon Johnson (D-1st), former federal prosecutor and CNN Legal Analyst Renato Mariotti, and Indivisible Chicago Executive Director Darcey Regan.

Similar protests took place in all 50 states and Washington, D.C.

The House of Representatives will vote on Wednesday on sending charges against the president to the Senate.

On Tuesday, House lawmakers held a contentious but comparatively collegial hearing to determine the length and terms of floor debate on two articles of impeachment against President Trump.

The House Rules Committee voted 9 to 4 along party lines to allow no amendments on the floor during the six hours of debate. The debate will be equally divided between the majority and minority, and controlled by House Judiciary Committee Chairman Jerry Nadler and Ranking Member Doug Collins or those they designate to do so.

There will be separate votes on Article I and Article II, and if the House votes to impeach, the House can consider a resolution appointing and authorizing the impeachment managers for the Senate trial.

If Mr. Trump is impeached Wednesday, it would be just the third impeachment of a president in U.S. history.

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Elsewhere in the Capitol, senators looked ahead to a potential trial in the upper chamber if the House votes to impeach. On Sunday, Senate Minority Leader Chuck Schumer wrote a letter to Majority Leader Mitch McConnell demanding several witnesses be called. McConnell responded to Schumer from the Senate floor on Tuesday, saying it was not the Senate’s role to go on a fact-finding mission.

Meanwhile Tuesday, President Trump listed no new arguments or requests but vented his frustrations with the impeachment process in a six-page letter to House Speaker Nancy Pelosi.

In a letter filled with exclamation marks and Trumpian verbiage, he offered his take the day before he likely becomes only the third U.S. president in history to be impeached.

“It is time for you and the highly partisan Democrats in Congress to immediately cease this impeachment fantasy and get back to work for the American People,” the president wrote. “While I have no expectation that you will do so, I write this letter to you for the purpose of history and to put my thoughts on a permanent and indelible record.”

Mr. Trump insisted that he’s being treated worse than the defendants in the Salem Witch Trials, which resulted in executions. He also accused Democrats, without evidence, of being guilty of what they are set to impeach him for.

“You are the ones interfering in America’s elections,” Mr. Trump wrote. “You are the ones subverting America’s Democracy. You are the ones Obstructing Justice. You are the ones bringing pain and suffering to our Republic for your own selfish personal, political, and partisan gain.”

The president is accused of two things: abusing his power for withholding aid from Ukraine to pressure the country to announce investigations that would benefit his reelection campaign, and obstructing Congress by not complying with its subpoenas throughout the impeachment process.

CBS News’ Grace Segers, Stefan Becket, Melissa Quinn, and Kathryn Watson contributed to this report.

(© Copyright 2019 CBS Broadcasting Inc. All Rights Reserved. CBS News contributed to this report.)