It's easy to imagine a cabinet post that oversees the NEA and other exisiting cultural organizations in the government and that uses the office to push for a renassiance of arts education in schools and the shoring up of cultural institutions across the country. Other countries, including the UK, have secretaries of culture or the equivalent. There are strong reasons for the US to have one, too. William Ferris of the Center for the Study of the American South at the University of North Carolina outlined those reasons in a recent New York Times op-ed.
You never know how petitions will fare in attracting attention and generating results, but the one inpired by Quincy Jones looks well worth signing and passing along. At least there's some change in the air right now, so the timing is certainly right.