Woods lost both of his matches on the first day at Medinah, despite making seven birdies on his own ball as he and Steve Stricker were beaten 1 up by Belgian rookie Nicolas Colsaerts and Britain's Lee Westwood in the afternoon fourballs.
In the morning session, Woods and Stricker lost their fourball match 2&1 to Ian Poulter and Justin Rose.
Both Woods and Stricker will sit out the third session at Medinah as Love's team look to extend their 5-3 lead over holders Europe.
"I think Tiger needs a rest, Steve needs a rest," Love said after Saturday's pairings were announced.
"We just don't want guys to be worn out. We need Tiger and Steve in the afternoon (for Saturday's fourball matches). We need Tiger and Steve on Sunday (for the singles).
"We just felt like we didn't want anybody to have to play five matches on this golf course. It's a big, long golf course. It's tough."
Woods has previously played in six Ryder Cups, compiling a win-loss-half record of 13-14-2 before this week.
"I didn't play very good this morning at all," Woods said of his opening match with Stricker at Medinah where he struggled badly off the tee. "I was hitting it awful and not doing anything well.
"But I hit it good this afternoon. I drove it great this afternoon and was in position, but we ran into a guy who just made absolutely everything."
Colsaerts was in scintillating form on his Ryder Cup debut, racking up eight birdies and an eagle in his first match for Europe as he and Westwood prevented the US from sweeping the four fourball matches.
- Steve Stricker