Rain on Wednesday postponed the opening matches for Del Potro and Japanese second seed Kei Nishikori, who had first-round byes, and halted two other men's matches at the $1.76 million hardcourt event.
Stephens is already trying to tamp down US Open expectations after beating current world number one Serena Williams on her way to the Australian Open semi-finals, where she lost to then-number one Victoria Azarenka.
Williams was playing in her first tournament since losing to Maria Sharapova in the third round of the Australian Open in January.
The No. 2-ranked Sharapova, who lost the final to Victoria Azarenka here last year before going on to win the French Open, faced only two break points in the match and she saved both of those in the first game.