LAKE BUENA VISTA, Fla. - The search for a 2-year-old boy dragged away by an alligator from an upscale resort at Disney World in Orlando late Tuesday evening has turned grim, as officials pulling alligators from the nearby lagoon and putting them down to check for the boy's body have so far not found him.

The effort near Disney's upscale Grand Floridian Resort & Spa was still considered a "search and rescue operation," said Jeff Williamson, a spokesman for the Orange County Sheriff's Department.

"We are very hopeful," he said at a morning news conference. "Sometimes you get the worst, but we are hoping for the best."

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Officials tell CBS affiliate WKMG in Orlando that they're going to "keep searching and searching and searching until we can't search anymore."

As the frantic search continues, CBS News confirms that Disney will be closing all of the resort beaches out of an abundance of caution, leaving many vacationers bewildered as they wait for news on the missing boy.

Nick Wiley with the Florida Fish and Wildlife Conservation said it's rare for people to be attacked by alligators, but he added that the creatures move around. He said four alligators were taken from the water overnight, but officials found no evidence they were involved. He said the alligators have to be euthanized before they are analyzed.

The family of four from Nebraska had arrived for vacation on Sunday, WKMG reports.

Witnesses said the family was on the beach of the Seven Seas Lagoon at about 9:20 p.m. and the boy's 4-year-old sister was in a play pen about 20 to 30 yards from the water on the sand, according to Orange County Sheriff Jerry Demings. The toddler was wading in the water nearby.

"The father actually went into the water to wrestle his son from the grips of the alligator," Demings said.

The attack happened in an area where "no swimming" signs were posted.

The alligator was estimated to be 4 to 7 feet long, but its exact size was not known, Demings said. The father suffered cuts and lacerations.

Florida Fish and Wildlife and an Orange County Sheriffs helicopter search for a toddler early Wednesday, June 15, 2016, after the boy was dragged into the water Tuesday night by an alligator near Disney's upscale Grand Floridian Resort & Spa in Lake Buena Vista, Fla. Red Huber/Orlando Sentinel via AP

The beach area is part of the luxury Grand Floridian resort, across the lake from Disney's Magic Kingdom theme park.

More than 50 law enforcement personnel searched the well-tended lagoon along with an alligator tracker and two marine units in an effort that continued through the night. Williamson said more personnel would be brought in Wednesday morning to offer some "fresh eyes" for the search.

Williamson said the boy was at the edge of the water, probably about a foot or two into the water, when the alligator attacked. The water was dark Tuesday night as searchers looked for the boy, Williamson said. They also used a sonar boat.

Williamson said Disney's boats were the first ones in the water.

Disney spokeswoman Jacquee Wahaler said everyone at the resort was devastated by what happened and Disney is helping the family.

When asked if Disney was aware of alligators on the property, Wahaler advised there were signs that said "no swimming."

Williamson brushed aside reporters' questions about the odds of rescuing the child at this point. "Right now, hopefully, we're searching for a little boy to bring the family some comfort," he said.

Demings said there had been no other recent reports of similar alligator attacks on the lake.

Jack Hanna, director emeritus of Columbus Zoo and Aquarium, told CBS News that Disney World is one of the safest places on the planet, but that alligators can be found almost everywhere in Florida.

"It's amazing how they can travel to get to another place to find food," Hanna said.

One of the questions officials should investigate is whether anyone at the resort had been feeding the alligators, thus drawing the animals closer to humans on the edge of the large lake where the boy was snatched.

Officials gather near a lagoon at Disney World's upscale Grand Floridian Resort & Spa, in Orlando, Florida, on June 14, 2016, after an alligator dragged a two-year-old boy into the water and disappeared. WKMG-TV

"If you look on a map you'll see it's a pretty extensive body of water," Wiley said of the lake being searched.

The Seven Seas Lagoon feeds into a series of canals that wind through the entire Disney property.

Minnesota residents John and Kim Aho, visiting Disney with their 12-year-old son Johnny, were stunned to hear what had happened to the child, whose name has not been released.

"We have been to Yellowstone and encountered grizzly bears, but this is just freaky," John Aho said.

Kim Aho said, their son is leery of the water around the park.

"He's a little freaked out about the gator," she said.

The Nebraska governor said his heart goes out to the family.

Their names have not been released, and Gov. Pete Ricketts' office said in a statement Wednesday that all they know was what they have seen in media reports.

Ricketts said "no family should ever have to experience such horror" and that he and his wife are praying for them.

In March 1997, a 3-year-old New Smyrna Beach boy was killed by a 450-pound alligator that grabbed him and dragged him into Lake Ashby in Volusia County as he walked on the shore with his dog. Officials believe the 11-foot gator was attracted by the dog. Adam Trevor Binford was pulled under the surface and drowned. Wildlife officials shot the alligator, which was still holding the boy's body 20 hours later.

The latest alligator attack comes amid what was already a tragic week in the Orlando area. On Sunday, a gunman opened fire at a gay nightclub in Orlando, leaving 49 victims dead in the worst mass shooting in modern U.S. history.