OLYMPIA — Substantial improvements in Washington’s financial outlook provided state lawmakers with a pathway to resolve their budget differences Tuesday, and negotiators expressed optimism they would avoid any government shutdown.In response to a revised forecast of state revenues, Senate leaders said they were OK finalizing a budget deal without policy overhauls that they had been seeking — so long as the House didn’t continue pushing for new revenue. House Majority Leader Pat Sullivan said lawmakers can work on a budget without additional revenue this year but will need to revisit the issue in the future in order to fully fund education.“It’s not as if the revenue debate is gone,” Sullivan said.Budget writers have some $300 million more in room to maneuver after Tuesday’s updated forecasts. That includes $110 million extra in the current budget cycle that would be available for one-time use in the next budget, an additional $120 million improvement in the revenue outlook for the next two-year budget cycle and $90 million in money available because of less reliance on government services.In total, the new coming 2013-15 budget will raise $32.66 billion — up about $2 billion from the current budget.The Economic and Revenue Forecast Council said it saw strong numbers in state building permits in the first quarter, saying housing has not been this strong in Washington since the end of 2007. However, forecasters cautioned that there remains a lot of uncertainty due to ongoing concerns about federal fiscal policy along with the economies of Europe and China.Budget negotiators have been struggling for months to find common ground on how to balance the state’s spending. With June 30 serving as the end of the current budget, state leaders have been rushing to identify which areas of state government would need to shut down — and which workers would need to be temporarily laid off — if the Legislature fails to reach a final compromise.