No, national ID cards would not make forgery more difficult, and in fact, it may make it easier. With national ID cards, a forger would only have to successfully forge one card, instead of the current fity or so (counting United States territories). Therefore, national ID cards would not stem forgery.
State Id cards and Driver license are already a huge target for forgery and creating a single national id card would only inconvenience citizens just on the bounds that there is forgery. A much simpler option would be the creation of a national standard that states would have to uphold.