Senate GOP aides, who are hoping to get a bill reauthorizing the No Child Left Behind Act on the runway early in the new year, are getting started on legislation that looks very similar to a bill Sen. Lamar Alexander, R-Tenn., the incoming chairman of the Senate education committee, introduced last year. (Cheat sheet on that legislation here.)

But there could be one major change: an end to the federal mandate for annual testing, Republican Senate aides confirm.

Instead the bill could leave decisions about testing schedules up to states. Some would likely stick with annual assessments, while others would try out gradespan testing and still others would mix and match, GOP aides say.

That’s an idea that’s likely to prove popular with education organizations, including the National Education Association and the American Federation of Teachers, both of whom have backed bills that would reduce testing requirements.

Getting the unions on board, even if it’s just behind the scenes, could help a GOP bill get to 60 votes in the Senate. Republicans are hoping to attract support from former Democratic governors now serving in the Senate, particularly those that aren’t so thrilled with the Obama administration’s NCLB waivers, which many perceive as inflexible, aides say.

But civil rights groups, such as the Education Trust, and U.S. Secretary of Education Arne Duncan aren’t likely to support the move away from annual testing. More on the arguments for and against annual state-wide assessments in this story.

If Republicans and unions are able to come together on a measure that gets rid of annual testing, it wouldn’t be the first time the NEA and the GOP have had a meeting of the minds. Back in 2011, the NEA helped garner support for an Alexander amendment to a 2011 NCLB reauthorization that would have given states a lot more flexibility in using school turaround dollars. (That broader NCLB renewal bill never made it over the finish line. But the language was enacted anyway, through a budget bill.)

An initial Senate Republican NCLB renewal bill would likely not include vouchers, since that could be a deal breaker for Democrats, not to mention some moderate Republicans, Senate aides say. A voucher amendment could instead be introduced on the Senate floor.

So would President Barack Obama be able to sign a bill that doesn’t include annual tests? It’s unclear. Duncan listed annual state-wide testing as one of his lines in the sand for ESEA renewal earlier this year.

But the next two years may present the administration’s best opportunity to influence NCLB over the long haul, since it’s unclear if a new education secretary—Republican or Democrat—would continue with the waivers.

The Senate’s preliminary timeline/game plan? Hold two quick hearings on NCLB early in the new year, and then have a bill marked up by Valentine’s Day and to the Senate floor shortly after that.