Blumenauer's bill, H.R. 6662, is not a VMT fee bill but a VMT 'study' bill, and it would be the Treasury Dept. that does the studying. Introduced on Dec. 13, it would require that other funding options be studied as well.
Pete Kasperowicz writes that according to Blumenauer, "$48 billion has been moved from the General Fund to the Highway Trust Fund over the last four years, but that the fund needs another $15 billion a year — on top of the gas taxes already collected — just to stay at 2009 funding levels."
As noted here, there was talk that the 'dreaded fiscal cliff' could spur consideration of a gas tax increase because of that $15 billion annual drain on the nation's dreaded fund' - talk which appears to have gone nowhere.
Kasperowicz references his March 24, 2011 article, "CBO: Taxing mileage a 'practical option' for revenue enhancement" where he described CBO's, "Alternative Approaches To Funding Highways" (PDF) report. "The report discussed the (VMT fee) proposal in great detail, including the development of technology that would allow total vehicle miles traveled (VMT) to be tracked, reported and taxed, as well as the pros and cons of mandating the installation of this technology in all vehicles", he wrote at that time.
Kasperowicz also references a 2011 draft transportation bill where the Obama administration appeared to support study of a VMT fee - a position he has clearly backed away from in 2009, unlike Rep. Bill Shuster, (R-PA), the incoming chair of the House Transportation Committee, who according to Bloomberg Business Week said that "a vehicle-miles tax, raising the gasoline tax, tolling and public-private partnerships should be among options Congress considers to close the (funding/spending) gap."
As for the major obstacle of implementing VMT fee proposals, protecting personal privacy by not tracking where motorists drive, according to Oregon Live, "Despite privacy concerns, Blumenauer said a national system would be convenient for drivers, protected personal privacy and easily administrable."