(CNN) The White House is urging Senate Republicans to preserve the option of moving to swiftly dismiss the charges against President Donald Trump after opening arguments in his impeachment trial, as GOP leaders and Trump's team look for a quick end to the proceedings, according to sources familiar with the discussions.

Republicans are debating including in the Senate resolution, which would govern the rules of the trial, a provision to dismiss the charges, something that would require 51 votes and would stop the trial in its tracks.

But moving ahead with a dismissal vote could put Republicans up for reelection in a tough spot if they are seen as moving too quickly to dismiss the case. Senate Majority Leader Mitch McConnell could not afford to lose more than two votes -- and GOP sources say the Kentucky Republican currently does not have enough votes to simply dismiss the case.

McConnell has made clear to his colleagues that he wants Trump to emerge victorious in the trial and is not willing to hold a vote that could fail, sources said. He's also keenly aware of what a vote to dismiss would look like politically, according to Republican senators, and has shepherded his conference away from the idea for several weeks.

Once the trial has begun, the Senate can vote on the merits of the articles of impeachment and choose to acquit Trump, something that can be done with only 34 votes because the Constitution requires 67 votes to convict the President and remove him from office. GOP proponents of this move argue Trump would have a stronger argument to say he was exonerated on the merits of the case, rather than simply relying on a procedural vote to dismiss the charges. Trump, though, might have to wait longer for a vote on acquittal to occur.

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