The U.S. Congress has been under divided partisan control for the past four years, with action on nearly every major piece of education legislation stalled as a result.

But analysts are split on whether a big change in the equation—what Republicans are hoping will be their takeover of the Senate—would break the logjam, and maybe even bring about a reauthorization of the Elementary and Secondary Education Act.

The GOP holds a solid majority in the House of Representatives, and Democrats control the Senate, with 53 seats to the GOP's 45. Two independents, Sens. Bernie Sanders of Vermont and Angus King of Maine, organize with the Democrats.

Republicans are expected to keep control of the House. But they hope to pick up enough Senate seats to tilt the scales in their favor, and races in such states as Montana, South Dakota, and West Virginia give them cause for optimism.

Divided government would remain no matter which party controls the Senate, with the White House in Democratic hands at least until President Barack Obama finishes his second term. But a new political calculation in Congress could spur movement on education bills, including an ESEA rewrite, some observers speculate.

"I think [a Republican Senate takeover] significantly increases the chances of reauthorization," said Andy Smarick, who served in the U.S. Department of Education under President George W. Bush. "I think we'll see actual energy behind this."

State officials, he added, are increasingly frustrated with the Obama administration's waivers from key provisions of the No Child Left Behind Act, the current version of the ESEA, and are likely to help spur congressional action on renewal.

But Charles Barone, who previously served as an aide to Democrats on the House education committee, argued that in the Senate, where the rules give the minority considerable leverage to block legislation, bills need some bipartisan support to proceed. And he doesn't think Sen. Lamar Alexander, R-Tenn., who would likely chair the education committee if the chamber flips to Republican control, is likely to compromise on K-12 policy.

"Alexander has stated pretty clearly that he would like to get the feds out of the business of doing education at all. Even if they had the majority, I'd be hard-pressed to see that [version of ESEA] sail through the Senate," said Mr. Barone, who is now the policy director of Democrats for Education Reform, a political action committee that supports candidates who embrace such policies as expanded charter schools and revamped teacher evaluation.

"It's not something Obama would sign either, so that's where that goes," he added.

Track Record

Sen. Alexander, a former U.S. secretary of education under President George H.W. Bush, has a long record on education issues, dating back to his stint as governor of Tennessee in the 1980s, when he championed one of the earliest experiments with merit pay for teachers.

He said in a recent interview that if Republicans take over the Senate and he is "fortunate enough" to take over the chairmanship of the Health, Education, Labor, and Pensions Committee, he would make ESEA reauthorization "a top priority."

The starting point would be a bill he introduced last year to renew the law, which garnered support from every GOP member of the committee, but didn't get a single Democratic co-sponsor.

The measure would significantly scale back the federal role in K-12 policy, allowing states to devise their own accountability plans and eliminate the federal role in requiring states to set specific student-achievement goals, or in identifying a certain percentage of schools as low-performing.

As under No Child Left Behind, schools would be required to test students in reading and math in grades 3-8 and once in high school, and report the results, including for subgroups of students, such as English-language learners and those in special education. Transparency would become the main lever for school improvement.

A similar measure passed the House without a single Democratic vote last year. But Mr. Alexander said he's prepared to seek input from the other side of the aisle.

U.S. Secretary of Education Arne Duncan "has states over a barrel with the need for waivers from unworkable requirements," Sen. Alexander said, which gives the federal Education Department too much power over state K-12 policy.

"I think there are a lot of Democratic senators whose constituents don't want a national school board," he added, invoking one of his favorite phrases.

Sen. Alexander has a history of working with Democrats to get changes to K-12 legislation that fly in the face of the Obama administration's priorities. When the Senate education committee was considering a renewal of the ESEA in 2011, for instance, Sen. Alexander and some Democrats, with the help of the 3 million-member National Education Association, teamed up on an amendment that seriously watered down the administration's signature School Improvement Grant program.

Funding Fights

If Republicans assume control of the Senate, Congress is almost certain to use the budget process to eliminate the Obama administration's favorite competitive-grant programs: Race to the Top, Investing in Innovation, and the SIG program, under which school districts compete within states for school turnaround money.

GOP lawmakers in the House have tried for the past few years to scrap those programs, but Senate Democrats have always championed them in budget negotiations.

They are probably going by the wayside if Republicans take over the Senate, leaving the administration with virtually no incentive money to help further its agenda.

"I think the federal government spends education money best when it empowers states to do things. That means fewer competitive-grant programs," Mr. Alexander said.

Renewed Focus

School choice legislation could also take on new prominence if the GOP takes over the Senate. It's become a signature issue for a number of high-profile Republican senators widely seen as having presidential aspirations, including Sens. Rand Paul of Kentucky and Marco Rubio of Florida, both of whom have written or co-sponsored school choice bills.

Sen. Alexander also has a school choice proposal, which would allow states to take almost all of their federal K-12 funds and combine them into one giant block grant aimed at creating scholarships for low-income students that could be used at any school, private or public.

He'd like that provision to pass, but wouldn't insist on making it a part of an ESEA reauthorization, since such tuition vouchers could repel support from Democrats and perhaps even some Republicans.

Mr. Alexander has also worked with Democrats, including Sen. Mary Landrieu of Louisiana, on a bill to revamp the federal charter-school-grant program. A similar measure passed the House with bipartisan support earlier this year, but the Senate has yet to act on it.

The charter bills' fortunes could improve no matter what the political landscape looks like, because the issue has bipartisan support, said Vic Klatt, a former aide to Republicans on the House education committee.

"The issue there is more a process one of whether the Senate will ever want to pass a targeted bill like that," separating charter legislation from the rest of the ESEA, said Mr. Klatt, who is now a principal at Penn Hill Group, a government-relations firm in Washington.

Lower-Profile Issues

And, no matter which party is in charge of the Senate, there's reason for optimism on education legislation beyond the ESEA. For instance, the Carl D. Perkins Career and Technical Education Act could be a relatively easy lift.

Other, lower-profile bills have a good shot too, including the Education Sciences Reform Act, which governs education research programs. A bipartisan measure to renew the law passed the House with broad bipartisan support earlier this year, but has yet to be taken up in the Senate. And aspects of the Higher Education Act reauthorization also have gained momentum in both chambers.

The political picture will change no matter who wins the midterm elections, since Sen. Tom Harkin, D-Iowa, the current chairman of the education committee, is retiring after this term. Sen. Patty Murray, D-Wash., is likely to take his place as the panel's chair or senior Democrat.

Sens. Murray and Alexander both are seen as dealmakers who are good at cross-aisle collaboration.

Ms. Murray, for instance, helped craft a budget agreement with Rep. Paul Ryan, R-Wis., and wrote a workforce-development bill that was signed into law this year.

And Mr. Alexander has a history of working with Democrats on education legislation, including the America Competes Act, which bolstered math and science education.

"Between the two of them, for the first time in a long time, I think there's some reason for optimism," Mr. Klatt said.