Your question, re; "... does the NRA really think that banning AK47's would make it hard to hunt deer?" I've hunted most of my adult life and have never seen or heard of anyone deer hunting with an AK-47. There are too many other choices that are far superior to the AK.

Private ownership of fully automatic AK-pattern rifles is strictly regulated by the National Firearms Act (NFA) of 1934. The Gun Control Act of 1968 ceased the import of foreign-manufactured fully automatic firearms for civilian sales and possession.

In 1986, an amendment to the Firearm Owners Protection Act stopped all future domestic manufacturing of fully automatic weapons for civilian use (non-military/non-law-enforcement). Fully automatic weapons are still manufactured in the US for military and law enforcement use however; automatic firearms manufactured domestically prior to 1986 or imported prior to 1968 may be transferred between civilians in accordance with federal and state law.

Semi-automatic AK-type rifles, are legal and obtainable in most states of the United States, however they may or may not be legal to own or possess depending on state, county, city, and local laws and ordinances. The 1994 Federal Assault Weapons Ban specifically banned the AK-47 by name, and many other such weapons (including obvious clones of AK-47's) manufactured after 1994 had to be modified to the letter of the law (removal of barrel threading, bayonet lug and folding stock). This ban expired in 2004, making all domestically produced semi-automatic AK-47s legal. The import of AK pattern rifles is still banned. However, certain states such as California, New York, New Jersey and Massachusetts have specific restrictions which effectively ban new purchases of many semi-automatic rifles, with some mentioning AK-pattern firearms by name.

The NRA has never condoned nor have they endorsed ownership of fully automatic weapons (AK-47 or otherwise) except by individuals possessing the proper federal credentials. The NRA is the major proponent of gun safety and education in this country. Over 55,000 NRA Certified Instructors now train about 750,000 gun owners a year.

The NRA does not even suggest that the AK-47 would be a good deer hunting rifle.

The AK-47 uses 7.62x39mm, a .30-caliber round producing about 1,500 ft./lbs. of energy at the muzzle, which is suitable for deer hunting at close range. This round is less powerful than all other .30 calibers commonly used for hunting. Specifically:
.30-30 Winchester, 1,900 ft./lbs.
.308 Winchester, 2,650 ft./lbs.
.30-’06 Springfield, 2,800 ft./lbs.
.300 Winchester Magnum, 3,600 ft./lbs.
.300 Weatherby Magnum, 4,200 ft./lbs.