The N64 was definitely saved by first party games. That machine failed because of the media format and the "3D or die" design among other things.
With the Gamecube on the other hand it's not completely lunatic to blame first party offerings imo. The console still survived largely because of first party games but they weren't enough to put sales at N64 level or higher despite much improved third party support. GC just didn't get a system seller like Super Mario 64 and that's were you could say that Nintendo failed.