All of the opposing votes came from Democrats.
Gov. Jon Huntsman Jr. probably will sign the bill this week, possibly today, education deputy Tim Bridgewater said.
"I am so relieved because this has been a serious issue for Utah," said HB1001 sponsoring Rep. Margaret Dayton, R-Orem. "We now have the option to focus on our own priorities."
For many GOP lawmakers, Spellings' letter reinforced their resentment of what they maintain is federal intrusion into the state's responsibility for education.
"I'd just as soon they take the stinking money and go back to Washington with it," said Rep. Steve Mascaro, R-West Jordan. "Let us resolve our education problems by ourselves. I will not be threatened by Washington over $76 million."
Spellings wrote that Dayton's bill itself doesn't jeopardize the money, but it may encourage Utah to defy No Child Left Behind provisions. Noncompliance would be costly, she warned.
HB1001 directs state school leaders to put Utah's education priorities ahead of NCLB mandates and authorizes them to ignore provisions that conflict with state priorities or cost state dollars.
NCLB requires schools to show annual test-score gains for all students, regardless of ethnicity, native language, disability or family income.
State school leaders and policy-makers want to use Utah's accountability system - called the Utah Performance Assessment System for Students (U-PASS) - to measure school quality.
Sen. Karen Hale, D-Salt Lake City, questioned whether lawmakers' priorities are in the best interest of students.
During the general session, the Legislature rejected the state Office of Education's request for $6 million to pay for tutoring of students who risk not getting a diploma because they failed the high school exit exam.
"That's part of our U-PASS system," said Hale, who ended up voting for Dayton's bill. "And yet we didn't prioritize it. We didn't fund that. So I'm really concerned that we are saying things are important and we have a great system, but we're not willing to fund it."
Bridgewater and other officials have spent the past few months negotiating with the feds for more flexibility under NCLB, namely to use U-PASS as Utah's accountability system.
HB1001's passage shouldn't threaten those discussions, Bridgewater said.
"We expect negotiations to continue," he said. "HB1001 has been helpful in getting the attention of the federal government. Now, it's about making sure states determine how they want to handle their own education systems."
That philosophy dominated floor debate, which lasted 90 minutes in the House.
House Majority Leader Jeff Alexander, R-Provo, said the bill cleans up a mess created when Congress passed NCLB in 2001. "I'm disappointed with our congressional delegation," he said. "Why did they pass it, and why don't they fix it? You start doing your work so we don't have to do it for you."
Lawmakers shot down proposals by Rep. Duane Bourdeaux, D-Salt Lake City, to add language that would ensure Utah tracks, reports and addresses the achievement gap.
Minority groups have stepped up their demands that the state do more to improve the academic performance of minority and disadvantaged students. They fear Utah's anti-NCLB sentiment could hinder that effort.
The House soundly defeated Bourdeaux's amendments, with many representatives calling them unnecessary.
Tribune reporter Rebecca Walsh contributed to this story.