I'm not aware of any program at present that does away with ground based infrastructure completely. Present plans are to have the ground based stations as a backup in case of a GNSS outage/interference.
The present FAA plan, for example includes DME while reducing the VOR coverage:
Navigation- En Route Transition; from FAA navigation Programs Update Sep 2013
As far as ground based navigational aids are concerned, the plan is to reduce the VOR coverage with VOR Minimum Operational Network (MON) as a middle step. However, the plan appears to be to retain DME at the expense of other Ground Based Navigation Systems (GBNS).
FAA's Alternative Positioning, Navigation, and Timing (APNT) project is geared up towards maintaining aviation operations in case of a GNSS outage. According to FAA:
The Alternative Positioning, Navigation, and Timing (APNT) project is investigating alternatives for providing higher precision back-up for Global Positioning System (GPS)-based position, navigation, and timing (PNT) services.
However, Ground Based Systems are still a part of the program (though VOR is not) and serve as a backup for the GNSS. One of the options is to modify the existing DME facilities in order to improve coverage/accuracy.
International Civil Aviation Organization (ICAO) 2013-2028 Global Air Navigation Plan also stresses the importance of having some 'conventional' ground based systems as a back-up for GNSS:
Conventional navigation aids (VOR, DME, NDB, ILS) are in widespread use globally, and most aircraft are equipped with the relevant avionics. The vulnerability of GNSS signals to interference has led to the conclusion that here is a need to retain some conventional aids or alternative navigation service solution as a back-up to GNSS.
ICAO also concurs that DME is the most appropriate ground based equipment to be used in the future navigation system:
The implementation of PBN will make area navigation operations the norm. DME is the most appropriate conventional aid to support area navigation operations(i.e. assuming DME multilateration on board capability),since it is currently used in multi-sensor avionics for this purpose.
At present, as far as I'm aware, there is no available roadmap for satellite/inertial only based navigation systems as far as civil air transport is concerned. Though GNSS will remain the primary means of navigation for the foreseeable future, plans still retain ground based systems as a backup.