Vitter's amendment would also cut funding for the head of any task force or council that is not subject to Senate approval.
Republicans trained much of their fire on Carol Browner, President Obama's energy and climate policy adviser. But Browner resigned in January to join the liberal Center for American Progress.
A similar measure to defund the administration's policy advisers passed the House earlier this year.
Here's more on Vitter's amendment and the presidential appointments bill.