VIDEO: Senate begins impeachment trial of President Trump with fight over the rules

The U.S. Senate will reconvene Tuesday and begin debating Majority Leader Mitch McConnell's proposed rules for the impeachment trial of President Donald Trump. You can watch a live feed of the proceedings below.

Should the Kentucky Republican's proposal pass, arguments would begin Wednesday morning. However, Senate Democrats plan to offer amendments to McConnell's resolution, Minority Leader Chuck Schumer (D-N.Y.) said Monday. At issue are the rules of evidence and the calling of witnesses. Democrats say the Republicans' proposed rules would severely hamper House managers' ability to submit evidence to the full Senate.

There is also continuing debate over which witnesses the mangers' should be permitted to call. Over the last few weeks, at least two people Democrats believe could have evidence harmful to the president's case — and did not testify before the House — have come forward to say they are willing to testify before the Senate if called.

Lev Parnas, a former associate of Trump lawyer Rudy Giuliani, has reportedly turned over documents that, he says, show the president pressured the Ukrainian government to announce an investigation into the family of former Vice President and Democratic presidential candidate Joe Biden. Parnas, facing federal charges that could see him serving prison time, has expressed a willingness to testify in the impeachment trial, USA Today reported.

Another witness Democrats have said they hope to call is former Trump national security adviser John Bolton. House Democrats never subpoenaed Bolton to testify, but he announced Jan. 6 that he would testify if subpoenaed by the Senate. Bolton's testimony could be crucial if rumors that he has crucial knowledge about the White House's dealings in Ukraine are true.

Republicans have responded to Democrats' demands about witnesses by vowing to call their own witnesses, potentially even Hunter Biden, son of the former vice president.

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The seven Democratic House impeachment managers appointed by House Speaker Nancy Pelosi (D-Calif.) will present the impeachment articles and evidence. Those managers are: Intelligence Chairman Adam Schiff (Calif.), Judiciary Chairman Jerry Nadler (N.Y.), and Reps. Zoe Lofgren (Calif.), Hakeem Jeffries (N.Y.), Val Demings (Fla.), Jason Crow (Colo.), and Sylvia Garcia (Texas).

The U.S. House voted Dec. 18 to impeach the president for abuse of power and obstruction of Congress. On Thursday, the House formally delivered the two articles of impeachment to the Senate.

President Trump's defense team, led by White House counsel Pat Cipollone and Trump's personal attorney, Jay Sekulow, will make the president's case. Two famous lawyers joined the president's team last week: Alan Dershowitz and Ken Starr. And on Monday night, the president added eight House Republicans to his defense team: Reps. Doug Collins (Ga.), Mike Johnson (La.), Jim Jordan (Ohio), Debbie Lesko (Ariz.), Mark Meadows (N.C.), John Ratcliffe (Texas), Elise Stefanik (N.Y.), and Lee Zeldin (N.Y.). These eight Republicans are expected to advise Trump's official defense team, but it is not clear yet if they will participate in the actual impeachment proceedings.