Diana Nyad in homestretch on way from Cuba to Fla.

Diana Nyad during Cuba-Florida swim, somewhere in Straits of Florida, on Sept. 1, 2013
Dawn L. Blomgren

Update: Diana Nyad completes historic swim from Cuba to Florida

KEY WEST, Florida U.S. endurance swimmer Diana Nyad's representatives say she's less than 2 miles from Florida in her latest attempt to swim there from Cuba, and they expect her to arrive sometime between 2 and 4 p.m. ET.

Around 11 a.m. on Monday, mere miles from Florida, Nyad called her support boats over and said she had "bad abrasions" in her mouth from her jellyfish-protection mask, according to her team.

While treading water, she said: "I am about to swim my last two miles in the ocean. This is a lifelong dream of mine and I'm very very glad to be with you. Some on the team are the most intimate friends of my life and some of you I've just met. But I'll tell you something, you're a special group. You pulled through; you are pros and have a great heart. So let's get going so we can have a whopping party."

Nyad is trying to become the first person to swim from Cuba to Florida without a shark cage. She says this will be her final try. Nyad recently turned 64.

In an online update posted before dawn Monday, her team said "Diana is on course to swim 112 statute miles. This is 35 more miles than anyone has ever swam."

Her team also claimed that a cruise ship decided to "make way" for her. They posted on Facebook Sunday afternoon that she had "swum farther north than the farthest end point of any of her previous attempts."

Diana Nyad
Diana Nyad's support boats sit in front of a cruise ship somewhere in the Straits of Florida on September 2, 2013.

On her blog, her medical team reported "Diana's tongue and lips are swollen causing her speech to be slurred. (Her doctors) are concerned about Diana's airways, but have not intervened."

With about 6.5 miles to go, Nyad was contacted by her support team, who were concerned she was cold and in pain. According to her team, she rebuffed offers to replace her swim cap, which fell off during the night, and instead kept swimming.

The 64-year-old is trying to become the first person to swim from Cuba to Florida without a shark cage. It's her fourth attempt in the last three years. She tried three times in 2011 and 2012.

Most of Nyad's previous attempts were derailed by run-ins with box jellyfish.

On this attempt, she was wearing a full body suit and custom face mask to protect against the venomous stings, reports CBS News' Elaine Quijano - though her team blogged late Sunday night that she hadn't used the mask to that point.

As of late morning on Monday, Nyad's team had only one reported sighting of box jellyfish, although it appeared to have not had any tentacles.

Nyad has said, "The box jellyfish takes you into an area of what I'd call science fiction. You feel like you've been dipped in hot burning oil. You burst into flames."