The Club for Growth, an influential conservative group, urged lawmakers on Monday to oppose a House GOP education policy overhaul on the floor this week to replace the No Child Left Behind Act.

The bill, H.R. 5, would give states and local school districts more authority over academic standards and testing instead of the federal government.

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But the Club for Growth said the 2001 No Child Left Behind Act should be repealed entirely, arguing the measure doesn't go far enough.

"Republicans deviated from their self-professed conservative principles in a huge way when they originally passed No Child Left Behind in 2001," Andy Roth, the Club for Growth's vice president of government affairs, said in a statement.

"If this week's bill was supposed to be an acknowledgement that the party is ready to return federal power to the states, then they have only given lip service to such an idea," Roth added. "Absent a plan that terminates No Child Left Behind, House members should demand that the bill allow states to completely opt out of the program."

The bill would also prevent the Department of Education from forcing states and school districts to adopt Common Core standards, which establish English and math benchmarks for all grade levels. Current law limits access to grant funding if schools don't opt into Common Core

Democrats will likely oppose the measure, which was written by House Education and the Workforce Committee Chairman John Kline (R-Minn.) and Rep. Todd Rokita (R-Ind.), because of the rollback of federal discretion over programs. 

The No Child Left Behind Act expired in 2007. Congress has yet to find a way to reauthorize it in the years since.