Delivering the GOP's weekly address, Alexander said Republicans would "work hard" with President Obama to eliminate their differences over a student loan bill, CBS News reported.
The House has passed a Republican-backed bill that would link the interest rates on student loans to the marketplace, an idea he said was "fairer to students and fairer to taxpayers."
Obama's proposal would also tie loan rates to the market, but Alexander said the administration's bill would not allow the rates to vary as much over the life of the loan.
The president has asked the House to redraw the bill.
Alexander, who served as secretary of education under President George H.W. Bush, said the GOP had "a major disagreement," however, with Democratic plans to create what he called a "national school board." Republicans, he said, favored local control.
Federal education policy has crated a "congestion of mandates," he said. Democrats on a Senate education committee recently voted to reauthorize a bill that would keep those mandates in place, Alexander said.
An alternative Republican proposal would emphasize state and local control, he said, and "puts Washington out of the business of deciding whether local schools are succeeding or failing."