Sen. Chris Murphy, D-Conn., argued on Sunday that the Senate has "a constitutional responsibility" to hold the impeachment trial of former President Donald Trump.

"There is clear precedent for the Senate moving forward on impeachment trial once being sent articles even after an official has left office, and so my analysis here sort of begins and ends with what is my constitutional responsibility," the Democratic senator told "Fox News Sunday."

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"I don't think our job ends just because the President has left office in part because impeachment comes not only with the provision to remove an official from office, but to disqualify them for future office so there is still a consequence to President Trump if convicted."

The Senate will take up an impeachment trial against Donald Trump for the second time on Tuesday after the House voted to impeach the former president last month.

The House voted to impeach Trump with a 232 to 197 vote on the charge of inciting an insurrection, with 10 Republicans joining all Democrats. It would take 17 Republicans joining all 50 Senate Democrats to convict Trump on the impeachment article, an outcome that is highly unlikely.

Late last month, Sen. Rand Paul, R-Ky., introduced a point of order claiming that it is unconstitutional for the Senate to hold an impeachment trial of a former president.  It was defeated by a 55-45 vote, with five Republicans joining all 50 Senate Democrats, meaning 12 additional Republicans would have to change their position in order for the conviction to succeed. 

Murphy argued on Sunday that Trump's impeachment trial "doesn't stop" the rest of the Senate’s business, saying that "the Senate can walk and chew gum at the same time."

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"We will next week," he told host Chris Wallace. "We will start off on Monday by confirming another cabinet nominee by the president."

"We will likely hold hearings and committees next week to move other nominees forward," Murphy continued. "And because last week we moved forward the process on the COVID relief bill that is going to save this country’s economy, we will also spend next week writing that legislation."

He stressed that "The Senate’s going to do all three things next week."

"We are going to do our constitutional responsibility and hold a trial," Murphy said, noting that "it won’t last very long." He went on to say that the Senate will also "move forward nominees and we are going to continue to push forward COVID relief legislation."

"The Senate can do all of those things and we will," he continued.

If Trump were convicted, the Senate could take up another vote to bar Trump from ever holding public office again. 

The Senate has never heard an impeachment trial for a president who was no longer in office, but Democrats argue removing Trump from the sphere of government is the main goal. 

Wallace asked Murphy on Sunday if he believes Trump incited the mob to attack the U.S. Capitol on Jan. 6.

"Even as the riot was occurring, the President had a chance to turn it around and instead he incited it knowing what was happening at the Capitol," Murphy argued. "So I think the case is absolutely clear, both in that rally at the White House and during the riot itself the President was taking steps to make it worse, not better."

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He added that he believes that once all the evidence is presented, "there'll be no choice but to convict," noting that he thinks the "conviction will be a bipartisan vote."

Fox News’ Morgan Phillips contributed to this report.