WASHINGTON — A bipartisan tax-and-spending plan designed to bring some normalcy to Congress’s budgeting after three years of chaos cleared its final hurdle on Tuesday when 67 senators voted to end debate on the measure and bring it to a final vote before it goes to President Obama for his signature.

The 67-33 vote easily surpassed the 60-vote threshold to break a filibuster and made way for final passage with a simple, 51-vote majority, likely on Wednesday. Republican support was surprisingly strong after days of uncertainty fueled by political posturing and Tea Party opposition.

The budget plan would restore $63 billion to defense and domestic programs in fiscal 2014 and 2015 from the levels they would have received if automatic, across-the-board spending cuts were to resume in January. Over 10 years, the plan would decrease cumulative deficits slightly by trimming military and federal worker pensions, extending a 2 percent cut to Medicare providers into next decade and making other changes, like ending federal research for some fossil-fuel discovery efforts.

Even its chief architects, Senator Patty Murray of Washington, the chairwoman of the Senate Budget Committee, and Representative Paul D. Ryan of Wisconsin, the chairman of the House Budget Committee, called the agreement a modest first step toward addressing the budget deficit in a more rational way. But its very modesty showed how difficult deficit reduction will be.