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Washington state lawmakers grappling over how to fill a projected budget shortfall of $5 billion may first have to end a stalemate on a more contentious issue: workers’ compensation.

There is widespread agreement in Olympia that lawmakers must do something to curb the surging costs within a state-run system that doles out billions in benefits, and Gov. Chris Gregoire said this week she doesn’t think lawmakers can leave the Capitol for the year without dealing with the issue. But the House and the Senate — siding with labor and business, respectively — have pushed competing proposals that won’t get consideration in the opposing chamber.