Sorenstam was 2 over par through the first nine holes of her second round, including three bogeys in a four-hole stretch. She was at 3 over par for the tournament after the front nine, two strokes over the projected cut.
Sorenstam, the best player in women's golf, made history Thursday by becoming the first woman in 58 years to play on the PGA Tour.
After a solid 1-over-par first round, Sorenstam started quickly Friday, sinking an 8-foot birdie putt at the 400-yard second hole. She saved par out of the sand with 5-foot putts on the first and third holes, and a 20-foot birdie putt at the 246-yard fourth hole stopped inches short.
But she bogeyed three of the next four holes.
If the projected cut held, Sorenstam would have to shoot 2 under or better on the back nine of the 7,080-yard layout to stay around for the weekend.
But no matter what happened, Sorenstam had already accomplished most of what she set out to do.
"Personally, I came here to test myself. I'm very proud of the way I was focusing and the way I made decisions and stuck to them," Sorenstam said after her opening 71 Thursday. "That's why I'm here. I wanted to see if I could do it. That's all that matters to me."
Sorenstam proved — at least for a round — that her game stacked up against the players on the men's tour.
About one-third of the golfers, the bottom third, reports CBS News Correspondent Steve Futterman, will be sent home after Friday's play. Still, she did better Thursday than 26 other golfers, including one of the top players in the world, Spain's Sergio Garcia, who shot a first-round 72.
Rory Sabbatini took advantage of a soft course after two days of rain for an opening 64. But Kenny Perry shot a 64 on Friday and was the early leader at 8 under par.
Defending champion Nick Price, who said her appearance on a sponsor's exemption "reeks of publicity," shot a 70.
"It looked like the way she's playing, she could easily compete on this level," Phil Mickelson said after his 67.
The top 70 players and ties advance to the final two rounds.
Playing partner Aaron Barber, a rookie on the tour, was impressed with Sorenstam's control.
"She handled her emotions and the nerves, the adrenaline, so well," he told CBS News Early Show co-anchor Harry Smith. "And I've never seen anyone hit the ball that straight before. She did so well. She hit so many greens. Under that kind of pressure, I think that's just amazing."
Barber feels Sorenstam has a good chance to make the cut, with the first-day jitters over.
"Everybody talks about how good it was for her to shoot one-over," he said. "She could have shot better. And I expect her to do that today. I certainly would not expect her to shoot any worse."
Barber said theirs is a supportive three-some.
"I remember after she made her first birdie, I kind of gave her a high five and I was walking up the green thinking, 'I've never done this before to a fellow competitor.'"
Everyone at her home golf course, the Lake Nona Country Club in Orlando, is behind her, too.
"Everyone's in full support of Annika here," Lake Nona golf pro Gregor Jamieson told CBS News Correspondent Peter King. "It's been quite something."
With a gallery that stood a dozen deep and strained to see every shot, Sorenstam showed how she has become the most dominant female golfer in 40 years. She won 13 times in 25 tournaments around the world last year.
She hit the ball right down the middle of the fairway on almost every hole, reports Futterman. Her putting turned out to be her big problem, making only one birdie putt.
She missed only one fairway during the first round here. And on the four greens she missed, she was close enough to use her putter.
Sorenstam might have been nervous Thursday — "My heart was beating, I felt a little sick in my stomach, my hands were sweaty," she said — but she never played like it.
The loudest cheer of the day came at the par-3 13th, where Sorenstam made her only birdie with a 15-foot putt from just off the fringe on her fourth hole of the day. She pumped her fist, kicked her leg and pointed to her caddie.
She stayed under par for 10 more holes, until three-putting from 60 feet at her 14th hole, the 470-yard fifth. That was the only fairway missed, but she then managed to get to the green from the right rough.
Sorenstam didn't go over par until missing an 8-foot putt on her final hole, the 402-yard ninth.
The last woman to play on the PGA Tour was Babe Zaharias in 1945. The last time there was this much interest in one round was when Tiger Woods made his pro debut in the 1996 Greater Milwaukee Open.
Hundreds of fans wore "Go Annika" buttons and held up signs urging her on.