The Briton faces Romania's 21st seed Simona Halep in the fourth match on Court 11 at around 23:00 BST.
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“I've just got to stay positive and make sure it stops now and goes the other way”
Heather Watson on her rankings slide from 39 to 76
Halep arrived in New York on the back of a win over Petra Kvitova in the New Haven final on Saturday.
"I've got a tough first round. She's had the best year of her career; she's won four tournaments already. It's not going to be easy," said Watson.
"But it's a Grand Slam and no matches are easy. I see every draw you get in a Slam as a good draw."
Watson has slipped to 76 in the rankings from a career high of 39 in February after missing two months with glandular fever, returning to play at the French Open at the end of May.
"I felt I came back too soon," admitted Watson. "But I didn't want to miss out on Paris and from then on, coming into Wimbledon, I wasn't playing enough tennis.
"There's no way you're going to play well without the work you put in and the hours. I didn't have a great Wimbledon or grass-court season.
"When you don't play you lose a bit of your eye for the ball and movement, and you're not as confident because you know you haven't played that much, and that was how I was feeling."
The 2009 US Open junior champion says she now feels fully fit and is enjoying working on developing a more attacking game with new coach Jeremy Bates.

Heather Watson factfile

  • Date of birth: 19 May 1992
  • Birthplace: Guernsey, Channel Islands
  • Started playing tennis aged 7
  • Moved to Nick Bollettieri Tennis Academy in Florida aged 12
  • 2009 US junior champion
  • Joined WTA Tour in 2010
  • Reached third round of Wimbledon in 2012
  • Current ranking: 76
  • Highest ranking: 39 (25 Feb 2013)
  • Best performance at US Open: First Round in 2011, 2012
"We've actually been coming in early and getting some good court time, working on a lot, coming in - he knows what he's talking about, especially when it's coming in and volleying," said Watson.
"He's such a nice guy and we get along really, really well."
Watson has recovered from the hip injury that kept her out of New Haven and denied her another opportunity to arrest the slide in her ranking that she admits is a concern.
"I'm totally worried about it," she said with a rueful grin.
"I try not to look at it but I'll have a peek and be like, 'Damn, I've gone from going up, up, up to coming down.'
"And I've never really come down, especially this much, so I've just got to stay positive and make sure that it stops now and goes the other way."
Second seed Victoria Azarenka begins her campaign against Dinah Pfizenmaier in Monday's night session at 00:00 BST, before world number one Novak Djokovic plays Ricardas Berankis.
Djokovic has made the last three finals at Flushing Meadows, winning the title in 2011, but had a relatively disappointing build-up this time as he lost in the semi-finals in Montreal and the quarter-finals in Cincinnati.
"This is a Grand Slam, so it is different from any other event," said the 26-year-old Serb. "I love playing Grand Slams.
"I had a very good record in US Open in the last five, six years that I have been coming back here, so I really look forward to it.
"I like the centre court. I like the atmosphere, the spirit of the court; it's suitable to my style of the game and the whole buzz that you feel around the US Open and around these courts."