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The NRA was established after the Civil War, and has had considerable influence on politics well before 1968. http://www.keepandbeararms.com/information/XcIBViewItem.asp?ID=3247 makes the argument that the NRA both did not fight the GCA itself, and advocated language in other bills which were reassembled into it:

KeepAndBearArms.com — The National Rifle Association has been called "the largest and oldest gun control organization in America" by more than a few gun owners. A fair amount of evidence supports their claim.
As the Gun Control Act of 1968 was nearing the President's desk, NRA was being accused by Senator Robert Kennedy (D-NY) of not supporting "any legislation to try and control the misuse of rifles and pistols in this country." Naturally, NRA needed to respond to the allegation, and they responded with great detail and unusual candor.
To deflect Senator Kennedy's assertion, NRA published an article by their magazine's Associate Editor entitled "WHERE THE NRA STANDS ON GUN LEGISLATION" — elaborating at length about NRA's longstanding support for a wide variety of gun controls that included gun and gunowner registration, waiting periods, age restrictions, licenses for carrying a firearm or having a firearm in your vehicle, increased penalties for violating gun laws, regulating ammunition and more.
Following are several telling quotes from the March 1968 American Rifleman — NRA's premier magazine, then and now — and brief analysis of a few of them. The complete article from which these quotes were taken can be found further below. Scanned images of this article are also linked below.
First, let's clear up the matter of NRA's support of NFA'34:

"The NRA supported The National Firearms Act of 1934 which taxes and requires registration of such firearms as machine guns, sawed-off rifles and sawed-off shotguns. ... NRA support of Federal gun legislation did not stop with the earlier Dodd bills. It currently backs several Senate and House bills which, through amendment, would put new teeth into the National and Federal Firearms Acts." —American Rifleman, March 1968, P. 22

Unless someone has evidence to prove that the NRA lied to its membership in its premier magazine, let the record show that the NRA got behind the first unconstitutional federal gun law in America and then bragged about having done so, many years later — decades after the law had been continually used to violate the rights of untold numbers of American citizens, including, surely, their own members.
The "Dodd" to which the above quote refers is the late Senator Thomas J. Dodd. Senator Dodd mimicked the Nazi Weapons Law of 1938, applied the underlying principles to the Gun Control Act of 1968, and took a leading role in getting the bill signed into federal law.

"The NRA supported The Federal Firearms Act of 1938, which regulates interstate and foreign commerce in firearms and pistol or revolver ammunition..." (P. 22)

The term "interstate commerce" is the BATF's fundamental justification for its firearms branch — a "color of law" excuse for the many assaults of innocent people they've conducted.

"The NRA supported the original 'Dodd Bill' to amend the Federal Firearms Act in regard to handguns when it was introduced as S.1975 in August, 1963. Among its provisions was the requirement that a purchaser submit a notarized statement to the shipper that he was over 18 and not legally disqualified from possessing a handgun." (P. 22)

That's one form of registration.

"In January, 1965, with the continued support of the NRA, Senator Dodd introduced an amended version of his first bill, now designated 5.14 and expanded to cover rifles and shotguns as well as handguns." (P. 22)

That's an extension of one form of registration to all types of guns not already under registration schemes at the time.