WASHINGTON — A bipartisan full-year funding bill took a big step forward in the Senate on Monday, despite opposition from Republicans who were denied chances to offer money aimed at addressing home-state problems like looming closures of air traffic control towers.

The legislation advanced on a 63-35 procedural vote that sets up a vote Tuesday to pass the measure and send it back to the House, which is likely to clear it later this week for President Obama’s signature.

Ten Republicans, including Maine Sen. Susan Collins, joined with Democrats to send the measure over the 60-vote hurdle set by Republicans. Maine Sen. Angus King, an independent, also voted in favor.

The sweeping 587-page measure would set a path for government in the wake of across-the-board spending cuts that took effect March 1 and prevent a government shutdown at the end of the month when funding for the day-to-day operations of every Cabinet department expires.

It covers the rest of the 2013 budget year, which expires Sept. 30.

The measure gives the Pentagon much-sought money for military readiness but also adds money sought by Democrats and Republicans alike for domestic programs.

While top Senate leaders like No. 1 Democrat Harry Reid of Nevada focused on the big picture – preventing a government shutdown – rank-and-file senators were sweating the small stuff, focusing on local concerns such as keeping meat inspectors on the job, preventing furloughs at rural airports and trying to ease layoffs at Army depots.

The opposition was led by Republicans such as Kelly Ayotte of New Hampshire – denied a vote on an amendment shifting $360 million to military readiness – and Jerry Moran of Kansas, who wants money to keep air traffic controllers at six small airports in his state.

There had once been speculation that the measure could be a potential vehicle to turn off painful across-the-board spending cuts of 5 percent to domestic programs and 8 percent to the Pentagon but now much of the focus is on bread-and-butter issues as facilities back home begin to absorb the cuts.