That's how tennis is. You have to be very careful. I have to make sure I put in a good performance.'
After seizing his number one ranking back from Rafael Nadal by winning Wimbledon, Federer is already under some pressure during the fortnight if he wants to keep his longtime honour.
The spot will remain in his possession by reaching the fourth round. But any early failure would throw the race open again, with new number two Andy Murray and number three Nadal then in with a chance.
Both Murray and Nadal could take the ranking by winning the title- should Federer fall in the third round.
2001 New York winner Lleyton Hewitt starts against Brazil's number 106 Thiago Alves, with the Australian now back just outside the top 30 a year after hip surgery.
German Bjorn Phau will try and derail Wimbledon finalist and fifth seed Andy Roddick in their opening-day meeting.
In women's play, second-seeded Serena Williams and number three Venus Williams open, with holder Serena facing American Alexa Glatch, whom she she beat last spring in Miami.
Venus gets Russian Vera Dushevina, while 2005 winner Kim Clijsters returns to Grand Slam play for the first time since her 2007 retirement, taking on Viktoriya Kutuzova of the Ukraine.