The onslaught ofis forecast to continue for the next few days, dumping as much as 50 inches on some parts of Texas.
Mandatory evacuations were announced by at least seven cities and eight counties before Harvey made landfall, but no such mandatory evacuation call was made for Houston, the nation's fourth most-populous city.
As Houston was inundated over the weekend, water rescues -- by truck, boat and Coast Guard helicopter -- of residents trapped by the floodwater numbered in the thousands.
Now, some residents are asking why they weren't told to get out of harm's way before the storm hit, leaving them stranded and waiting for help.
Many were brought to a shelter set up by the American Red Cross at the George R. Brown Convention Center, but the 1,300 cots set up for evacuees quickly filled up. More facilities were being prepared Monday morning, with additional shelters being arranged in other cities, including Dallas and San Antonio. The Federal Emergency Management Agency said Monday they expect more than 30,000 displaced people to be placed in temporary shelters.
On Sunday evening, Houston Mayor Sylvester Turner stood by his decision not to order a mandatory evacuation of the city. He said the best course of action was for residents in Houston and surrounding areas to stay in place. Factors in his decision included not knowing exactly where Harvey (when it was still a hurricane) was headed, and the "crazy" logistics of trying to plan an evacuation of 2.3 million people within a couple of days.
Turner also cited the experience the city had when residents evacuated ahead of Hurricane Rita in 2005, leading to, leaving many people stuck in traffic for more than 20 hours as they tried to flee the city, resulting in dozens of deaths. Rita had been predicted to hit Houston, but ended up making landfall well east of the city.
"The decision that we made was a smart one," Turner said. "It was the right decision in terms of their safety, and always we must put the interests of the city of Houston, and Houstonians, first."
Texas Governor Greg Abbott is sending more than 3,000 National Guardsmen to help with rescue efforts. Abbott had urged people to leave the area before Harvey arrived, but did not criticize local officials for failing to order a mandatory evacuation of Houston.
Abbott told CBS News correspondent Mark Strassmann, "Well the evacuation calls, of course, are up to local officials, and now is not the time to second-guess the calls they made. My job is to work with them and assist them in any way possible to make sure we save as many lives as we can."
Abbott told "CBS This Morning" co-anchor Norah O'Donnell on Monday that, "the time for making that determination has passed; no need for us to relitigate that issue right now."
"What we have to focus on, again, is making sure that we continue this evacuation process, get people out of harm's way, get them relocated, and then begin the rebuilding process," Abbott said.
When asked about the federal government's response to the disaster, FEMA Administrator Brock Long -- referring to Hurricane Harvey as a "landmark event" -- said that it was up to Texas state authorities to set mission priorities.
"All disasters begin and end at the local level," he said. "The bottom line is, is that it starts at the local level. When the local government's capacity has been exceeded to handle the disaster and what they're facing," he said that is when further resources were called upon from the county or state governments, before asking for federal assistance.
Two people have died as a result of Hurricane Harvey.
Editor's Note: An earlier version of this story stated that Governor Abbott "did not demand a mandatory evacuation for Houston." A spokesperson for the Governor's office stated that in Texas the governor does not make such orders.