Gregoire declined to say what her proposal looks like, but says that it addresses all of the contentious issues that are currently in play between both sides, plus one new idea which she also wouldn't discuss.
Gregoire said that there's continued progress, and that "no one's given any indication of walking away" from the negotiation table.
But she stressed that while they're closer than they were at the beginning, talks are "tenuous."
"The negotiations are tenuous," she said. "I'm just being honest with you."
Lawmakers are more than halfway through a 30-day special session to address the budget. They are trying to close a roughly half-billion dollar shortfall for the two-year budget cycle ending June 2013.
Gregoire said that if they aren't able to reach a general agreement by Tuesday, it will be difficult for lawmakers to get everything done by the April 10 end of the 30-day special session.
Sen. Joe Zarelli, the Senate Republicans' leader on budget issues, said that while lawmakers have moved closer together, "we're still trying to get agreement on those bigger moving pieces."
"The focus is around whether we just write a budget and get out of town or if we take the opportunity to fix some things with real reform," he said.
Senate Majority Leader Lisa Brown said that she plans to have all of the members of her caucus back early next week to discuss the plan.
"Clearly everyone has to go back to their caucuses and see how it resonates," she said of Gregoire's plan. "Next week, we simply try to resolve all those issues and hopefully we're done."
Also Friday, Republican gubernatorial hopeful Rob McKenna said he'll unveil an outline of budget-related ideas on Monday, the timing of which was questioned by Gregoire.
"Why weren't those ideas brought up to us two months ago, or a month ago or two weeks ago?" she asked. "We're making good progress and everyone's at the table and working in good faith, and I don't need somebody external who doesn't understand all the issues and hasn't been a part of the discussions to throw a monkey wrench in it."
McKenna's campaign said that he's only releasing a budget policy paper with ideas on creating a sustainable budget for the future.
"It's as simple as that," said McKenna campaign spokesman Charles McCray. "The idea that we're trying to inject ourselves into the negotiations is false."
McKenna and Democratic former U.S. Rep. Jay Inslee are vying to replace Gregoire, who is not running for a third term.
Zarelli said he'll be interested to hear what McKenna's ideas are, saying that if he has a suggestion that could help resolve some of the issues they're facing, it's "always welcome."
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