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Mrs. Angle said she will work to defund the agency if elected, and has vowed to challenge the federal government’s constitutional standing to set education policy under the 10th Amendment.

Mr. Raese told The Times earlier this month that the department “has failed miserably.”

“I think it’d be better off just giving every state $1 billion. You’d be ahead,” he said. “When you look at outcomes-based education, when you look at school-to-work, No Child Left Behind, the list is endless of failures.”

As the idea appears to gain momentum and legitimacy, some Republican incumbents on the campaign trail are highlighting the movement to eliminate the department.

“There’s not a hint in the Constitution that we ought to have it,” Rep. Roscoe G. Bartlett, Maryland Republican and a member of the House’s Tea Party Caucus, said during a panel discussion last week. “And there’s not a shred of evidence that it’s done anything to improve education.”

Democrats say the push to cut the department highlights the radicalism of tea party candidates.

In Colorado, freshman Sen. Michael Bennet, a Democrat, has aired ads featuring a video of Republican challenger Ken Buck saying, “We don’t need a Department of Education.”

Republicans accuse Mr. Obama and other Democrats of exaggerating the threat that tea-party-backed candidates pose to education programs and the Education Department.

“Instead of having an honest discussion about bringing back fiscal responsibility to Washington, D.C., the president is setting up a straw man with his claims about education funding,” said Rep. John Kline of Minnesota, who is in line for chairman of the House Education and Labor Committee if Republicans take control of the chamber.

No Child Left Behind is due for reauthorizing, and Mr. Obama, in an interview published Monday, told the National Journal that he hopes to get Republicans’ cooperation on that, whatever the outcome of the election.

Critics of eliminating the Education Department also say the move would reduce the federal budget by just 6 percent, and that lower-income Americans would be hurt the most by the move. For example, eliminating or downsizing the agency could end or reduce Pell Grants for college students and the Title 1 program for schools and districts with large numbers of students from lower-income families.

Jennifer Marshall, director of domestic policy studies at the Heritage Foundation, said the key issue in measuring the value of a separate federal department for education is “how to get money and decision-making back closest to the child.”

She said the conservative think tank has praised congressional efforts to allow states to apply only once a year for federal funding, instead of for each program.

“Right now, the red tape far outweighs the 10 percent of funds that come down,” she said.

c Stephen Dinan contributed to this report.