It is unclear if any federal power authorizes such a requirement: the Supreme Court's decision in United States v. Lopez (1995), which struck down the Gun-Free School Zones Act as unconstitutional, made clear that private citizens and education are not inherently commercial enterprises subject to federal regulation under the Commerce Clause. (That decision was reaffirmed in United States v. Morrison (2000), which dismissed a federal lawsuit alleging violence between college students, as beyond federal jurisdiction).
My guess is that Obama will try to get around those decisions by conditioning federal grants to school districts on their mandating unpaid service by students. (The Supreme Court hasn't struck down a spending-condition since United States v. Butler (1936)). Prior to the election, Obama supporters also spoke of sweetening the pot for college students (but not other students) by giving them a tax-credit in exchange for the community service.The Obama Administration has temporarily put these plans for mandatory service on the back-burner.
Legal commentator Walter Olson of Overlawyered writes that after he publicized the Obama community-service requirement, and his post "began drawing thousands of visitors, the Obama website administrators at change.gov silently replaced the 'require' language with something new and different: 'Obama will call on citizens of all ages to serve America, by setting a goal that all middle school and high school students do 50 hours of community service a year and by developing a plan so that all college students who conduct 100 hours of community service receive a universal and fully refundable tax credit ensuring that the first $4,000 of their college education is completely free.'"