But CBS News Correspondent Jacqueline Adams reports that this all-American hero might break the record under a cloud.
With number 53, McGwire inched closer to breaking the record. But if he makes it, if he passes the magic number 61, McGwire's accomplishment may be tainted because he's admitted using a performance-enhancing substance called androstenedione, nicknamed andro.
"It's legal stuff sold over the counter. Anybody can go in there and buy it. There's absolutely nothing wrong with it," says McGwire.
Major league baseball and the St. Louis Cardinals' medical staff agree, saying that androstenedione is a natural substance that has no proven anabolic steroid effect.
Andro does raise a player's testosterone level and is intended to build lean muscle mass and promote a speedier recovery from injury. But because it is classified as a nutritional supplement, it has not been tightly regulated the way steroids are.
McGwire and major league baseball athletes may think andro is just fine, but the NFL, the NCAA, and the International Olympic Committee have all banned it.
Just last month, Randy Barnes, the Olympic shotput champion, was banned from his sport for using andro.
Nutritionist Dr. Richard Rivlin worries that McGwire's successes may prompt kids to begin using the stuff.
"Since Mark McGwire is a role model for many youngsters," says Dr. Rivlin, "they may be taking androstenedione in excessive amounts and that could interfere with the normal development of puberty."
Not much research has been done on andro, but some doctors fear that since it behaves like a steroid, it could cause some of the same side effects - which may include sterility, liver cancer, and acne.