Bush has said he will oppose any attempt to compel aides to testify in public and under oath in continuing inquiries into whether the sacking of the prosecutors was politically motivated.
The senate committee authorised subpoenas of Karl Rove, Bush's chief political strategist, along with Harriet Miers, former White House counsel, and William Kelley, deputy White House counsel.
"I know [Bush] is 'the decider' at the White House. He is not the decider for the United States senate"
Patrick Leahy, senate judiciary chairman
Bush has offered to have aides meet officials under a number of conditions.
Patrick Leahy, a Democrat who chairs the judiciary committee, said: "We're told that we can have a closed-door meeting with no transcript, not under oath, a limited number of people and the White House will determine what the agenda is.
"That, to me, is nothing ...
"I know [Bush] is 'the decider' at the White House. He is not the decider for the United States senate."
Without a compromise between Republicans and Democrats a lengthy court fight could ensue, possibly lasting until after Bush leaves office in January 2009.
Any court battle could refer to the issue of executive privilege, a legal doctrine that shields presidents and their aides from having to answer questions or turn over information to congress or grand juries.
Tony Snow, White House spokesman, said the administration had made a "good-faith" offer.
"The offer is on the table. [If] they issue subpoenas, it's off the table. But they haven't issued subpoenas," Snow said.
One of Rove's former aides replaced one of the fired prosecutors, who later told sacked colleagues that the administration might retaliate if they complained.
Recently released documents show that prosecutors were judged on such factors as their effectiveness as well as loyalty to Bush and Alberto Gonzales, the US attorney-general.