Not to my knowledge on a national level. There is only so much the Feds can do without amending the Constitution. There are four states that require licenses to buy any firearm (Hawaii, Illinois, Massachusetts, and New Jersey) and an additional four that require a license for handguns only (Iowa, Michigan, Nebraska, and North Carolina). Why Handguns only? Well, handguns are actually the classification of firearms most likely to be used in firearm related crimes. The most recent numbers I've seen attribute 5,600 criminal deaths to handguns, where as only 246 are attributable to semi-automatic rifles and slightly fewer were attributed to Shotguns/Bolt Action Rifles.
While many nations do have liscensing systems for gun ownership for various purposes, this may not be an easy law to implement in the states due to being an unreasonable restriction under the 2nd Amendment (I'm not aware of any states challenges rising far enough to test that validity) and would be hard to pass, let alone defend. States that have strict guidelines and are "May Issue" states (meaning that even if you meet all the qualifications, the decision maker can still say no because... reasons...) tend to reverse the decision on first appeal as they would rather quietly give you the license than let the complaint rise to a level where a court is ruling against the law.
At this time, I'm not aware of any group actively calling for this on a national level, though the Federal Government does not have much of a say in automotive licensing so if there is a group working towards this, they would be working at a more local level.