"It's not whether it's me - it's anyone. Just because I won last year, it's nothing to do with that. It's just more for the guys that have to play this evening, and you have guys that have two days off between matches.''
Title rivals Rafael Nadal completed his first-round match on Monday, while top seed Novak Djokovic and five-time winner Roger Federer both wrapped up their openers on Tuesday.
Del Potro goes on to face 2001 champion Lleyton Hewitt, who beat Brian Baker 6-3 4-6 6-3 6-4.
Williams, the US Open champion in 2000 and 2001 and seven-time grand slam winner, went down in a three-hour, second-round clash with China's Zheng Jie.
Zheng advanced to the third round against Spain's Carla Suarez Navarro, outlasting the American 6-3 2-6 7-6 (7-5) in a victory she called unbelievable.
At three hours and two minutes, it was the equal fifth-longest women's singles match in US Open history.
As a result of Wednesday's downpours, organisers postponed eight women's second-round singles matches and 20 doubles encounters until Thursday.
One held over was the second-round clash between women's champion Serena Williams and Galina Voskoboeva of Kazakhstan.
The rain meant some matches that started at 11am were being completed as darkness fell.
Agnieszka Radwanska and Li Na managed to beat the rain to reach the third round.
Third-seeded Radwanska defeated Maria-Teresa Torro-Flor 6-0 7-5, while Chinese fifth seed Li beat Swede Sofia Arvidsson 6-2 6-2.
Radwanska, who has never gone beyond the fourth round, next plays Russia's Anastasia Pavlyuchenkova and Li - in her 30th grand slam - will face 30th seed Laura Robson in a rematch of their clash 12 months ago, which the British player won.
Robson defeated France's Caroline Garcia 6-4 7-6 (7-5).
Among men's seeds to exit were Italian No.16 Fabio Fognini, who lost 6-1 6-2 6-2 to American Rajeev Ram.
Jurgen Melzer, the 29th-seeded Austrian, slumped in straight sets to Russia's Evgeny Donskoy while Alex Bogomolov sent French 24th seed Benoit Paire packing in five sets.
Croatian Ivo Karlovic put America's James Blake into retirement with a 6-7 (2-7) 3-6 6-4 7-6 (7-2) 7-6 (7-2) victory.