Collaborative for Student Success, which is supported by the Bill and Melinda Gates Foundation and other charities, published a memo Friday criticizing Jindal's position on the education standards as motivated by a desire to win the Republican presidential nomination.
In the memo, Executive Director Karen Nussle notes that Obama administration first started promoting Common Core five years ago, yet Jindal only filed a lawsuit against the federal government this week.
"Now, just 16 months before the kickoff of the Iowa Caucuses, there is suddenly a Constitutional case to be made against the Common Core," she writes.
The memo is a major salvo from supporters of Common Core, a movement to standardize what children in different states are taught in basic subjects like math, science and history.
Though started by governors from both parties in the 1990s, the program has become less popular in recent years as the Obama administration sought to use federal funding and waivers to encourage states to adopt it, and as students and parents have complained about its implementation.
Jindal's lawsuit was one of the more high-profile attacks on Common Core so far. In the suit, he charged that the Obama administration's push violated the 10th Amendment protection of states' rights because it was overly coercive.