Senate Health, Education, Labor and Pensions Committee Chairman Lamar Alexander (R-Tenn.) with ranking Democrat Patty Murray (Wash.) at a hearing on Capitol Hill. (Susan Walsh/AP)

The top Republican and Democrat in the Senate on education issues struggled to reach common ground in the difficult business of writing a law to replace No Child Left Behind.

But on the Senate floor Wednesday, they diverged during debate on their bipartisan legislation over a topic that has long separated the political parties: school vouchers.

Sen. Lamar Alexander (R-Tenn.), a former governor and education secretary under President George H.W. Bush, proposed an amendment to the education bill that would allow low-income students to use federal tax dollars to pay private school tuition.

And Sen. Patty Murray (D-Wash.) offered a lengthy rebuttal, arguing that Alexander’s idea would undermine public education.

Alexander’s amendment was defeated by a vote of 45 to 52, with some Republicans joining Democrats to vote it down, including Sens. Kelly Ayotte (N.H.), Susan Collins (Maine), Mark Kirk (Ill.) and Lisa Murkowski (Alaska).

Alexander called his plan “the most ambitious proposal ever to use existing dollars to enable states to offer school choice.” It would allow students whose families meet the federal definition of poor to get $2,100 each in federal funds to be used for private school tuition.

The program would cost $24 billion a year and serve as many as 11 million students, said Alexander, who proposed that the funds be taken from federal dollars now spent on K-12 education.

The voucher money, which represents about 40 percent of federal education money, could be used for a wide variety of public, online or private schools, including religious schools.

He pointed to a successful model for his idea in the Pell Grant program, the popular federal program that gives grants to low-income students to be used for higher education, including public and private universities and colleges.

“Last year, $31 billion in federal Pell grants followed students to public and private colleges,” Alexander said.

“Our elementary and secondary education system is not the best in the world,” he said. “U.S. 15-year olds rank 28th in science and 36th in math. I believe one reason for this is that while more than 93 percent of federal dollars spent for higher education follow students to colleges of their choice, federal dollars do not automatically follow K-12 students to schools of their choice.”

“Instead, money is sent directly to schools,” Alexander said. “Local government monopolies run most schools and tell most students which school to attend. There is little choice and no K-12 marketplace as there is in higher education.”

Despite its success in higher education, “voucher” remains a bad word in much of the K-12 education establishment and the idea hasn’t spread rapidly, Alexander said. He said his idea would “help children move up from the back of the line, allow states to use federal dollars to create 11 million new opportunities to choose a better school.”

The idea of using federal money for private school vouchers and other education alternatives has long floated around Republican policy circles, but the recent spurt in new voucher programs in states has encouraged GOP lawmakers in Congress.

Critics, including most Democrats, teachers unions and groups such as the National School Boards Association, say “school choice” sounds good but can pour tax dollars into private hands with little accountability and uncertain educational outcomes.

Murray argued against Alexander’s proposal, saying that it would divert scarce dollars meant for the country’s poorest students to private schools.

“Vouchers might cover some, but usually not all, of the tuition at a private school,” she said. “In some cases, a voucher would make just a small dent in the full cost of a private school. That would enable students from more affluent families the ability to afford private schools, because they have the means to make up the difference. But students from low-income backgrounds would still be priced out of that choice.”

What’s more, studies of voucher programs in Milwaukee and the District of Columbia have shown that they do not improve students’ academic achievements, she said. “Study after study has shown that vouchers do not pay off for students or taxpayers,” Murray said.