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Last month, the Fairfax School Board and four Fairfax County delegates sent letters to Mr. McDonnell urging a veto.

Delegate Timothy D. Hugo, Clifton Republican, blames school districts for what he sees as a tardy reaction to the legislation.

“Fairfax County did a poor job of letting the delegates and senators know this was a problem,” said Mr. Hugo, who joined fellow Republican delegates David B. Albo of Springfield, Barbara J. Comstock of Fairfax and Thomas Davis Rust of Herndon in sending the letter to Mr. McDonnell.

“The real problem is that these school boards didn’t get engaged on it,” Mr. Albo said. “They never really lobbied hard, so we had to, kind of on the fly, create enough stink to get some no votes on it.”

Mr. Jones admitted that the VEA did not oppose the bill until Jan. 31 — midway through the legislative session. Once it became apparent that it wouldn’t be accompanied by state funding, there was “gnashing of teeth,” he said.

“If you ask, should we provide more PE, everyone says, ‘Yes,’” Mr. Jones said. “But then if you turn around and ask the question, ‘Should we provide more PE but students won’t get any computer instruction?’ that’s different.”