Efficient Use of Government Spectrum Act of 2012

Efficient Use of Government Spectrum Act of 2012 - Directs the President, within five years after enactment of this Act, to withdraw or modify the assignment to a federal government station of electromagnetic spectrum between the frequencies from 1755 to 1780 megahertz. (Currently, such frequencies are occupied by the Department of Defense [DOD] and other federal agencies.)

Requires the President, if a federal government station cannot be relocated from such spectrum without jeopardizing essential military capability, to modify the station's assignment of such spectrum to permit shared federal and non-federal use.

Directs the Federal Communications Commission (FCC), within three years after enactment of the Middle Class Tax Relief and Job Creation Act of 2012, to: (1) reallocate such spectrum for commercial use; and (2) as part of the competitive bidding auctions required by such Act, grant new initial licenses, subject to flexible-use service rules, for the use of such spectrum, paired with the spectrum between frequencies from 2155 to 2180 megahertz already designated for auction.

Directs the proceeds attributable to the competitive bidding of the 1755 to 1780 megahertz range to be allocated in the same manner as other specified frequencies pursuant to such Act for uses including reimbursements to agencies for relocation and sharing costs, the building of the nationwide public safety broadband network, and deposits or reimbursements to the U.S. Treasury.