The Senate’s version of a $10 billion education jobs package, which looked like it was on life support just a few days ago, has now cleared an important procedural hurdle, smoothing the way for final passage in that chamber.

Senators today voted 61-38 to cut off debate on the measure, meaning that it can receive final consideration. The bill, which would provide aid to states to prevent what supporters warn would be thousands of teacher layoffs, includes some offsets to education programs, albeit not to key administration priorities, such as Race to the Top.

The bill would trim $82 million from student aid administration, $50 million from the Striving Readers program, which finances adolescent literacy programs, and $10.7 million from Ready to Teach, which helps provide telecommunications programs for educators.

Once the Senate officially passes the bill, the House of Representatives, which passed a different version of the bill earlier this summer, would still need to approve the Senate measure before it could become law. But the House is scheduled to be on recess until the middle of September, so it may be a while (and at least several weeks into the school year) before cash could begin trickling down to financially-squeezed districts.