Senate Majority Leader Harry ReidHarry Mason ReidBiden fails to break GOP 'fever' Nevada governor signs law making state first presidential primary Infighting grips Nevada Democrats ahead of midterms MORE (D-Nev.) pled for civility Tuesday as the Senate began its formal debate on Supreme Court nominee Elena Kagan. 

In floor remarks Tuesday morning, Reid asked senators to maintain the civil nature of the debate over Kagan, who is now the country's solicitor general.

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"As the debate moves to the Senate floor and as we move toward a final vote, I look forward to a continuation of the passionate but civil discussion we saw in committee," Reid said while praising the debate over Kagan's nomination before the Senate Judiciary Committee. 

Reid hopes to move to a final vote by the end of the week before the Senate recesses for August. 

The promised support of five Republican senators — Richard Lugar (Ind.), Lindsey GrahamLindsey Olin GrahamOVERNIGHT ENERGY:  EPA announces new clean air advisors after firing Trump appointees |  Senate confirms Biden pick for No. 2 role at Interior | Watchdog: Bureau of Land Management saw messaging failures, understaffing during pandemic Graham, Whitehouse: Global transition to renewables would help national security Hillicon Valley: Senate unanimously confirms Chris Inglis as first White House cyber czar | Scrutiny mounts on Microsoft's surveillance technology | Senators unveil bill to crack down on cyber criminals MORE (S.C.), Susan CollinsSusan Margaret CollinsSenate confirms Radhika Fox to lead EPA's water office Pelosi says she's giving Senate more time on Jan. 6 commission Overnight Energy: Schumer to trigger reconciliation process Wednesday | Bipartisan bill would ban 'forever chemicals' in cosmetics | Biden admin eyes step toward Trump-era proposal for uranium reserve MORE (Maine), Olympia Snowe (Maine) and Judd Gregg (N.H.) — has made it close to certain that Kagan will be confirmed.

One Democrat, Sen. Ben Nelson (Neb.) has said he will vote against Kagan — but he assured his party that he would break a filibuster of her nomination if need be. 

Sen. Jeff SessionsJefferson (Jeff) Beauregard SessionsThe Hill's Morning Report - After high-stakes Biden-Putin summit, what now? Border state governors rebel against Biden's immigration chaos Garland strikes down Trump-era asylum decisions MORE (R-Ala.), the senior Republican on the Judiciary Committee, has not taken the possibility of a filibuster off the table, but has said that such a move is highly unlikely. 

Debate over Kagan before the judiciary panel was spirited, but not heated. 

Before Kagan's confirmation process as solicitor general last year, Reid said Kagan testified that she would bring an "'understanding of how to separate the truly important from the spurious'" to her job. 

"In the final days of this process, I suggest we keep those words in mind," Reid said.