Party chairman Roy Herron told reporters at a news conference that he was especially concerned by a report that the state chapter of the American Federation for Children is spending $800,000 to lobby for a large-scale school voucher program in Tennessee.
Critics, particularly Democrats, have said that voucher programs take needed funds from public schools and give them to private schools.
An official familiar with the federation's plans told The Associated Press last week that the group is using the money on broadcast television, cable and radio advertising. The official spoke on the condition of anonymity because the group has not made the amount public.
"This is another battle in the Republican war on public schools," Herron said. "Vouchers may benefit vultures, but they take from Tennessee taxpayers and leave our children and our state worse off."
Republican Gov. Haslam told reporters last week that he plans to stick with the narrower plan he proposed in his State of the State address, which he predicted would be hotly debated anyway.
Haslam's proposal would limit the program to 5,000 students in failing schools in the academic year that begins in August, and grow to 20,000 by 2016.
"We didn't just decide to pick a point where we thought, 'Oh, this can get passed,'" Haslam said. "We really did pull a lot of people in to go through a thoughtful process about what we think is right for Tennessee right now."
Haslam declined to say whether he would veto a bill that significantly goes beyond his proposal.
The measure is scheduled to be heard this week in the education committees of the House and Senate.
Herron said he also is against the governor's plan.
"We've had folks who have wanted to raid the public pockets time and time again, and this is one more time where that's the case," he said.
A recent telephone poll of 650 Tennessee residents conducted by Middle Tennessee State University showed state residents pretty much evenly split on the governor's voucher proposal.
"Statewide, it's too close to call," said Ken Blake, director of the poll, which has a four-percentage-point error margin. "Opponents of the plan outnumbered supporters in our sample, but it's unclear whether the same is true among all Tennesseans. They appear evenly, or nearly evenly, divided."