It will not. You don't want perfidious FedGov meddling, what is enacted by the pen of one administration is rescinded by the pen - or sword - of the next.
The perfidious meddling of the federal government is not involved in the Drivers Licence Compact
http://en.wikipedia.org/wiki/Driver_License_Compact (which, BTW, does not include all 50 (57 by some counts) states). And it is not a "national recognition" compact - rather, it creates a method for states to exchange traffic infraction information in order for the collection of fines/costs from drivers who would otherwise ignore citations from other than their home state on the dual theories of "they can't pull my license if I don't liver there" and "my insurance company will never know".
Driving, which as we all know only too well is but a privilege, does have some nebulous connection to commerce between, among, and through the various states. The Commerce Clause is regularly hauled out to explain to places like NJ, NY and Ca (most frequently) why they cannot force out-of-state drivers to get a separate license valid for transit through their territory. That probably does not qualify as perfidious federal meddling.
Commerece, such as the hauling of cheap (and sometimes inexpensive) Chinese goods from a distribution enter in one state to retail outlets in another state, is considered by the population of the country to be "essential". Strangely, the keeping and bearing of arms, let alone the hiding of handguns from common observation, is not seen as being anywhee nearly as essential. Change that and you will achieve recognition of any one state's permission slip as being equivalent and as valid as that state's own permission slip. And it will not require the perfidious meddling of the federal government, although there is some possibility that once it comes about they could see various ways of controlling it via the distribution of money extorted from the residents of one state to the residents of some other state.
There are a few other details involved, but that's a fair nut-shell explanation of what it will take.
stay safe.