There was, though not to nearly the same extent we see today and the level of polarization. In the mid-1960s, Senator Thomas Dodd began pressing for legislation that would restrict the sending of firearms through the mail (of particular importance to many Americans since this was how Oswald obtained his Carcano rifle with which he shot JFK in November 1963). While the NRA was often reluctant to work with anyone to enact any firearm provisions, it did work with Dodd to amend the Federal Firearms Act, to say that anyone purchasing a gun through the mail had to enclose an affidavit certifying their name, age, felon status, address, plus some other identifying information, that was then forwarded to the local law enforcement agency. However, Dodd, as a Democrat, was more or less driven to align himself with Lyndon Johnson when he was elected in 1964, and outlined his own gun bill, soon to become the Gun Control Act. The new Dodd Bill prohibited anyone from purchasing guns through the mail except to licensed dealers, imposed new restrictions on importing foreign guns, raised the age to buy a handgun to 21 from 18, and made the age to buy shotguns and rifle 18.
The NRA made the claim that this bill would lead to the complete disarmament of all guns in America. Other gun-rights organizations, like Guns and Ammo also pushed their agenda that the Dodd Bill was a slippery slope. LBJ and Robert Kennedy, among many others, of course, refuted the claim as ludicrous. In 1965, the NRA VP Franklin Orth testified before a Senate committee as to the reputation and history of the NRA, and of its belief that such a law would only burden law-abiding citizens.
At this point, the vast majority of the American public and political leaders supported further gun legislation, and the Watts Riots in August 1965 further accentuated this. By the time of Charles Whitman's killing spree, again, American favored something to be done. The only thing largely standing in the way was that no solid, single gun-control organization existed that could drive home a bill. While the NRA had constituents pour in letters, phone calls, and publish pamphlets and articles opposing gun measures. By 1968, the NRA had a membership of over 900,000.
What finally pushed the bill over the edge to the floor, was the assassination of Martin Luther King, Jr. on April 4, 1968. The subsequent killing of Bobby Kennedy two months later also became a catalyst. By this point, even celebrities endorsed the bill (oddly enough, including Charleton Heston). On October 22, 1968, the Gun Control Act, or GCA was passed, which expanded federal control over interstate gun sales, new regulations on obtaining a dealer license, and further amended the restrictions on who could purchase guns.