OLYMPIA - Like the faithful waiting for a smoke signal that a new pope has been chosen, lobbyists, state officials and lawmakers have spent 15 days in special legislative session looking for a sign that the $600 million budget deadlock between Republicans and Democrats has been breached and everyone soon can go home.

And this may be it: a hopeful signal in the unlikely form of a 30-year-old contractor from Spokane. Adding to his growing reputation as the 54th Legislature's Mr. Fixit, Republican Rep. Todd Mielke has been called in to negotiate a package of tax cuts - perhaps the single biggest obstacle to adjournment.

"I take it as a positive step," said Senate Ways and Means Chairwoman Nita Rinehart, D-Seattle, who negotiates money matters on behalf of the ruling Democrats in the Senate.

But it's progress not seen by the public. While lawmakers continue their much-ballyhooed, first-ever, open-door, budget negotiating sessions, tax-cut talks are taking place behind closed doors.

"Right now we're talking just generic dollar amounts rather than specific proposals," Mielke said.

But already the Senate has presented a written tax-cut proposal to the GOP-controlled House and both sides have discussed which of the 26 different tax cuts on the table are "must haves," Mielke said.

It was House Republicans who forced the closed budget negotiating sessions into the open. House Speaker Clyde Ballard, R-East Wenatchee, says he's not sure where or how the huge gap between the House and Senate plans will be negotiated.

Senate leaders, who went to the open sessions reluctantly, have no objection to the current closed one-on-one negotiations between Rinehart and Mielke.

"We like to point out to them it's not in a public setting," said Senate Majority Leader Marc Gaspard, D-Puyallup.

Mielke, the GOP House caucus chairman, is viewed as having a special relationship with the large class of GOP newcomers in the House - the folks who have said compromise on the budget would be a defeat. Outside of the session, he is head of the House GOP campaign operation and recruited and raised money for many of the new members.

"So far I'm impressed that he has a good grasp of where all his members are coming from," Rinehart said.

Mielke demurs: "That's a nice assumption to make. I just wish it were true."

Already, though, Mielke has been credited with brokering the biggest deal of the year, the repeal of much of the 1993 health-care-reform act. He has also been called in to try to jump-start stalled discussions on welfare reform.

Senate Democrats have regularly attacked the GOP newcomers in the House for their intransigence and ultraconservative ideology. Twice in the past two weeks Senate leaders have invited the press in to issue dire predictions about what would be wrought unless Republicans begin to compromise.

Republican leaders have said little in response.

Yesterday, though, Gaspard said there is no reason to worry yet about lack of progress in the session. He and Rinehart said they will become worried if there has been no movement by May 15 - when local school districts send out layoff notices if a budget has not been approved.

And Rinehart and Ballard said they think the guts of a budget deal may emerge as soon as week's end.

It will be a tough job. Budget negotiators have met for weeks with no major agreements. The House wants to spend $17.3 billion in the 1995-1997 budget; the Senate proposes $17.9.

The House wants to cut taxes by about $738 million; the Senate proposes about $265 million.