(CNN) Pam Jones said the water crept up on them with shocking speed.

It started to pour in through the garage of her elderly parents' home in Dickinson, Texas, where the family had gathered to ride out Hurricane Harvey. Within hours three feet of it swamped the home, trapping Jones, her 83-year-old mother and 86-year-old father upstairs. They called for help.

That was Saturday.

Jones and her family weren't rescued until Sunday. They weren't found by the Coast Guard but by a volunteer with a boat

"We're really blessed," Jones said afterward.

Since Hurricane Harvey slammed the region, thousands of residents like Jones have been plucked from their homes. But each rescue has underscored broader questions about the disaster's true scope.

In all, 53 Texas counties issued emergency declarations -- an area that's home to around 11.4 million people. How many people successfully fled their homes ahead of the storm? How many are still waiting to be rescued?

"At this time, we don't know," FEMA director Brock Long said Thursday.

There are compelling reasons for the lack of answers.

On Thursday, six days after the storm first made landfall, the Houston Fire Department was set to begin a door-to-door mission in southwest Houston in hopes of finding residents still waiting to be plucked from the floodwaters.

Lt. Gen. Russel Honoré -- who oversaw relief operations in New Orleans after Hurricane Katrina in 2005 -- said that officials won't know the true scale of the disaster until that door-to-door search is complete. Honoré said that it was during those searches after Katrina that authorities in New Orleans "really found the bad news."

"The worst is yet to come in terms of the outcome, which means people stuck in their homes and we can't get them out, and they're isolated," he said.

Immediate rescues take priority

Photos: Hurricane Harvey slams Texas Downtown Houston is seen behind the flooded Buffalo Bayou a few days after Hurricane Harvey came ashore in August 2017. The Category 4 storm caused historic flooding. It set a record for the most rainfall from a tropical cyclone in the continental United States, with 51 inches of rain recorded in areas of Texas. An estimated 27 trillion gallons of water fell over Texas and Louisiana during a six-day period. Hide Caption 1 of 22 Photos: Hurricane Harvey slams Texas NASA astronaut Jack Fischer photographed Hurricane Harvey from the International Space Station. Hide Caption 2 of 22 Photos: Hurricane Harvey slams Texas Steve Culver comforts his dog Otis in the hurricane aftermath. Harvey destroyed most of his home in Rockport while he and his wife were there. Hide Caption 3 of 22 Photos: Hurricane Harvey slams Texas Houston police officer Daryl Hudeck carries Catherine Pham and her 13-month-old son, Aiden, after rescuing them from floodwaters. Hide Caption 4 of 22 Photos: Hurricane Harvey slams Texas A damaged home is seen in the Key Allegro neighborhood of Rockport. Hide Caption 5 of 22 Photos: Hurricane Harvey slams Texas A car is submerged by floodwaters on a freeway near downtown Houston. Hide Caption 6 of 22 Photos: Hurricane Harvey slams Texas Melani Zurawski cries while inspecting her home in Port Aransas, Texas. Hide Caption 7 of 22 Photos: Hurricane Harvey slams Texas A graveyard is flooded in Pearland, Texas. Hide Caption 8 of 22 Photos: Hurricane Harvey slams Texas Soldiers with the National Guard patrol Rockport, looking for residents trapped in their homes. Hide Caption 9 of 22 Photos: Hurricane Harvey slams Texas Evacuees are loaded onto a truck in Houston. Hide Caption 10 of 22 Photos: Hurricane Harvey slams Texas People push a stalled pickup through a flooded street in Houston. Hide Caption 11 of 22 Photos: Hurricane Harvey slams Texas Rockport residents return to their destroyed home. Hide Caption 12 of 22 Photos: Hurricane Harvey slams Texas Rescue boats fill Tidwell Road in Houston as they help flood victims evacuate the area. Hide Caption 13 of 22 Photos: Hurricane Harvey slams Texas People wait to be rescued from their flooded home in Houston. Hide Caption 14 of 22 Photos: Hurricane Harvey slams Texas Volunteers in Dallas organize items donated for hurricane victims. Hide Caption 15 of 22 Photos: Hurricane Harvey slams Texas When Harvey slammed the Texas coast and flooded much of Houston, volunteers sprang into action. Some came from as far away as the Florida Everglades, boats in tow, ready to rescue people trapped in their homes. Hide Caption 16 of 22 Photos: Hurricane Harvey slams Texas Larry Koser Jr. and his son Matthew look for important papers and heirlooms inside a flooded home in Houston. Hide Caption 17 of 22 Photos: Hurricane Harvey slams Texas Members of the National Guard rest at a furniture store in Richmond, Texas. Hide Caption 18 of 22 Photos: Hurricane Harvey slams Texas Volunteer rescue workers help a woman from her flooded home in Port Arthur, Texas. Hide Caption 19 of 22 Photos: Hurricane Harvey slams Texas This aerial photo shows flooded residential neighborhoods in Houston. Hide Caption 20 of 22 Photos: Hurricane Harvey slams Texas Tammy Dominguez and her husband, Christopher, sleep on cots at the George R. Brown Convention Center, where thousands of people were taking shelter in Houston. Hide Caption 21 of 22 Photos: Hurricane Harvey slams Texas An elderly patient waits to be rescued from the Gulf Health Care Center in Port Arthur. The facility was evacuated with the help of first responders and volunteers. Hide Caption 22 of 22

Disaster relief efforts typically have three phases: rescue, recovery and rebuild, according to Honoré. The coastal Texas region still sits largely in the rescue phase, which means that immediate issues of food, water and shelter come first.

"This is very much still a life-saving, life-sustaining response effort," two senior FEMA officials said Tuesday.

JUST WATCHED Trapped mother: We're out of food and water Replay More Videos ... MUST WATCH Trapped mother: We're out of food and water 00:47

Among the hardest-hit communities is Houston, the fourth-largest city in the country, with a metropolitan area population of 5 million.

Houston police had responded to more than 5,000 rescue requests by Wednesday afternoon, Police Chief Art Acevedo said. More than 10,000 people have been saved by federal rescue teams, FEMA director Brock Long said. And those totals don't include the unknown numbers saved by volunteer groups and neighbors.

US Air Force Maj. Gen. James Witham, the National Guard's director of domestic operations, said that planning the response to this storm was "very different" than that for previous disasters.

"Normally, we plan a response for that first 72 hours (or) 96 hours, the weather passes, then we're really into recovery mode," he said. "We will be doing life-saving and life-sustaining efforts for a much longer period due to the nature of this storm."

Lt. Col. Travis Walters, public affairs officer for the Texas Military Department, said that operations are becoming "more methodical" as they move into the second phase of the relief efforts.

"We are beginning as more resources pour in to do more methodical search and clear operations," he said. "Move into a neighborhood, clear the entire neighborhood, make sure it's clear of people so we save lives, then move on to the next place. That's what we're dedicated to doing."

Those searches will be a "huge undertaking," said Houston Fire chief Samuel Peña. The southwest part of Houston, where the searches will begin Thursday, has 16,000 single-family homes and 2,500 multi-family homes, he said.

"We expect to find people in these areas. Some of them have made it up to the attic and that's where they've been waiting for a rescue," Peña said.

As the death toll continues to rise, Houston Police chief Acevedo said he was well aware of the bad news that might lie ahead.

"We just continue to pray that once the water starts receding and we're able to do secondary searches and complete assessments of the interior of homes and businesses that the body count -- that we know will rise -- doesn't rise significantly," he said.

Acevedo said authorities had received 60,000 to 70,000 calls for help during the storm. During an average day, it handles about 8,000, the Houston Office of Emergency Management tweeted. Because of the "overwhelming" number of calls, 911 responders are keeping a log that prioritizes those most in need of assistance, and helping those people one by one, he said.

The Coast Guard, which is attempting to lighten the load on Texas 911 call centers, was receiving over 1,000 emergency calls per hour, Commandant Admiral Paul F. Zukunft said.

Scale of devastation unprecedented

The sheer physical size of the area that has been drenched and battered by the monster storm is also slowing assessments of its impact.

CNN meteorologist Gene Norman said the area in and around Houston that has received more than 10 inches of rain is approximately the size of the state of Kentucky -- roughly 39,728 square miles. That's larger than Belgium, Greece, or Bangladesh.

Hurricane Harvey has broken the US record for rainfall from a single storm, CNN senior meteorologist Dave Hennen said. The storm dumped almost 52 inches of rain in parts of Texas, and the coastal cities of Beaumont and Port Arthur got pummeled with 26 inches of rain in 24 hours.

Large swaths of Houston, the fourth-largest city in the country, remain underwater. Up to one-third of Harris County -- where Houston is located -- was underwater through Sunday and Monday, according to Harris County Flood Control District meteorologist Jeff Lindner.

Lindner said that the unprecedented nature of the flooding has complicated understanding what would happen next.

"We just don't know exactly how this is going to play out because it's never happened before," he said.

Agencies, volunteers in massive rescue effort

Volunteer Adam Brackman said he had rescued about 75 stranded people from Sunday to Tuesday. He said he was able to save one man who had been stranded in a factory for three days with little food or water.

"There was a huge group of people who came together and were coordinating on the ground," Brackman said.

Brave volunteers like Brackman are playing an integral part of the all-hands-on-deck rescue operations. They put their own lives at risk to help those in need. But that vital effort lacked clear lines of coordination, making it even more difficult for officials to accurately assess the numbers rescued -- and the numbers still stranded.

JUST WATCHED Woman trapped on roof with no food or water Replay More Videos ... MUST WATCH Woman trapped on roof with no food or water 00:45

The US Coast Guard, Customs and Border Patrol, local police departments and emergency responders have been joined by regular citizens with boats. Louisiana's Cajun Navy , a group of volunteers that formed in the wake of Hurricane Katrina, has been conducting water rescues in the Houston area.

Those rescues have partly relied on information from Zello, a walkie-talkie app that has been used to connect those needing help with those Cajun Navy organizers. Others have used the website Houston Harvey Rescue . The site allows those needing a rescue to describe their predicament, give their location and ask for help.

User Still others trapped in their homes took to Twitter or Facebook with requests for help.User @haleeyjay_ posted a call for help on Wednesday morning on Twitter. She gave her address and said her phone was at 9 percent battery and that she was 35 weeks pregnant. "Please keep calling for me," she wrote, "water is waist deep."

Other Twitter users responded to say they had called emergency responders to help her -- and a few hours later @haleeyjay_ said she was safe.

But not everyone was so lucky, and Brackman said he feared for those who he wasn't able to reach.

"The hardest thing was at the end of the day when it gets dark and you need to stop for safety, and knowing that there's someone who's stuck up there in the attic for another night is really disheartening," he said.