The US Congress' most powerful Democrat is coming under pressure from Senate allies as she holds up President Donald Trump's impeachment trial.
House of Representatives Speaker Nancy Pelosi has delayed sending the articles of impeachment to the Senate in a tussle over rules with Republicans.
Senator Dianne Feinstein called on Mrs Pelosi, her fellow California Democrat and ex-neighbour, to "send it over".
The Senate's Republican leader vowed there would be "no haggling".
Mitch McConnell said he can muster the majority of 51 votes needed among his fellow Republicans in the Senate to codify the proceedings without Democratic support.
Senate Democrats said prolonging the stand-off would be pointless.
"The longer it goes on the less urgent it becomes," Senator Feinstein said on Wednesday, Bloomberg News reported.
"So if it's serious and urgent, send them over. If it isn't, don't send it over."
The political trial of Mr Trump cannot begin until the Democratic-controlled House sends its articles of impeachment, the charges against the president, to the Senate.
Senator Chris Coons, a Delaware Democrat, told Politico: "I respect the fact that [Pelosi] is concerned about the fact about whether or not there will be a fair trial, but I do think it is time to get on with it."
Senator Jon Tester, a Montana Democrat, said: "I don't know what leverage we have. It looks like the cake is already baked."
Joe Manchin, a West Virginia Democrat, also said he believed it was time to start the Senate trial.
Mr Trump was impeached by the House in December on allegations of abuse of power and obstruction of Congress.
The Republican president is accused of withholding military aid to pressure Ukraine to investigate his political rival, Democratic presidential front-runner Joe Biden.
Democratic leaders have argued that witnesses and new documents should be allowed in the Senate trial.
They have also criticised Mr McConnell for saying he would work in "total co-ordination" with the White House during the proceedings.
Mrs Pelosi said in a letter to fellow Democrats on Tuesday that she would not send the articles of impeachment across the Congress building until Republicans "immediately" publish their proposed rules so "we can see the arena in which we will be participating".
Mr McConnell said the rules would be "essentially the same" as those for the 1998 impeachment trial of Democratic President Bill Clinton, which also began without an agreement on witnesses.
Speaking on the Senate floor on Wednesday, Mr McConnell said: "There will be no haggling with the House over Senate procedure. We will not cede our authority to try this impeachment."
He accused Mrs Pelosi of wanting to keep Mr Trump "in limbo".
Mrs Pelosi's counterpart in the Senate, Chuck Schumer, and House Democrats have stood by her.
Mr Trump is the third president in US history to be impeached.
The Senate is unlikely to come up with the 67 votes needed to remove him from office given that his fellow Republicans control the chamber by 53 votes to 47.
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