However, Gregoire said she wouldn't give up on the goal of having a budget passed by midnight Thursday, when the regular 60-day legislative session is scheduled to end.
"I'm not going to give up, we're going to keep working," she said.
Gregoire said it's possible lawmakers could have a budget deal before Thursday but might have to come back for a one-day session to pass the plan.
Doubt over lawmakers' ability to get a budget passed increased after Senate Republicans took control of the Senate floor Friday night and passed their own budget plan early Saturday morning. That budget, as passed, has no chance of passing the House, where Democrats hold a 56-42 majority.
Democrats hold a 27-22 majority in the Senate, but Republicans were able to seize control and pass their own plan with the help of three conservative Democrats.
On Monday, Senate Minority Leader Mike Hewitt, R-Walla Walla, sent House Speaker Frank Chopp, D-Seattle, a letter saying he would like to work "toward agreement on a sustainable budget that supports the core priorities of state government."
Senate Democrats' budget writer, Sen. Ed Murray of Seattle, said Tuesday that ideas are moving between the House and Senate and governor.
"Ideas are not being rejected outright," he said. "The possibility for movement is there. We just need people to have a chance to look at some of these things before the day is out and see if we can reach an agreement."
The Republicans' plan makes deeper cuts to state programs than either House or Senate Democrats' original plans do, especially in health and human services programs. It also proposed $74 million in cuts to schools and colleges.
More than 50 protesters on Tuesday afternoon crowded outside of the office of Republican Sen. Joe Zarelli of Ridgefield, who wrote the GOP budget plan. Chanting "Hey Zarelli, you can't hide, don't play politics with our lives."
Zarelli was at the Capitol and not in his office.
"It's always the case that you have a handful of people who want you to do something that's just not possible," he said later. "And they don't want to accept the facts around that."
In a statement issued Tuesday, Republican Attorney General Rob McKenna, who is running for governor, called for a bipartisan budget compromise, saying that the "state can't afford to have the Legislature go into yet another special session instead of fulfilling its most basic duty of completing a budget on time."
McKenna, who is facing Democrat Jay Inslee in the race to succeed Gregoire, said that any budget compromise should ensure that public education should be the first priority for funding.
On Monday, Inslee criticized the Republican budget's proposed cuts to education, saying that the plan would take "us backward at a time we must focus on the future and restoring our commitment to our children's education."
Lawmakers are looking to close a budget gap of about $500 million through the end of the two-year budget cycle ending June 2013. Because Gregoire wants reserves of at least $500 million dollars left, lawmakers are addressing a $1 billion problem.
AP writer Jonathan Kaminsky contributed from Olympia.