But Jim DeMint, president of the Heritage Foundation, was a major proponent of A-Plus when he was a senator. And Walker said he believes allowing the vote would cause outside groups to rescind their key votes, even if it does not pass.
That is particularly important to leadership because the measure is unlikely to draw much Democratic support, and passing it with only Republicans could be a heavy lift because a sizeable chunk of members likely will refuse in principle to vote for a bill retaining the federal government's role in the education system.
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Rep. Virginia Foxx, a senior member of the Education Committee who also is the vice chairwoman of the Rules Committee, said the latter panel may allow a few other amendments to be voted on.
"We still have several amendments that we haven't heard, so we've got to work on some amendments," she said. "There may be some new amendments."
Among the amendments that weren't heard was an especially controversial plan from Rep. Luke Messer that would change federal public-school funding to a voucher system and allow students to spend that money at private schools.
"I don't know if we'll be able to get that amendment in order before the vote comes up in July or not," he said. But, he added, "I will not withhold my support based on whether or not I get a vote on broader school-choice options."
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The House's renewed interest in the education bill comes as the Senate prepares to debate and vote on its own version of a No Child Left Behind rewrite. That differs significantly from the House's bill by retaining a larger federal role in schools. It was carefully negotiated by Sens. Lamar Alexander and Patty Murray, the top Republican and Democrat on the Health, Education, Labor, and Pensions Committee. It strikes the kind of balance that makes both Republicans and Democrats uncomfortable.
Education advocates have long thought that Senate action would spur the House to act on its own version, teeing up a conference committee that likely will pull the Alexander/Murray bill to the right. But some conservatives already are upset that the House bill doesn't allow states to opt out of No Child Left Behind completely. They will definitely be on edge about a conference committee that, in their minds, would water down the already weak House bill.
In the Senate, the debate will focus on keeping together the group of legislators that already compromised quite a bit to come up with their initial deal. "It will be bipartisan coming to the floor. There are amendments that could divide that bipartisan coalition in a hurry," said Senate Minority Whip Richard Durbin about the upcoming floor debate.
The Senate bill retains language under current law that some Republicans dislike that requires states to use two federal tests per year in math and reading in the third through eighth grades. There likely will be an attempt on the Senate floor to reduce those testing requirements.