The combination of wind and rain is flooding some homes to the ceilings and ripping away part of the roof of the Superdome, where thousands of people have taken shelter.
Katrina weakened overnight to a Category 4 storm and turned slightly eastward before hitting land about 1110 GMT on Monday east of Grand Isle, near the bayou town of Buras, providing hope that New Orleans would be spared the storm's full fury.
But National Hurricane Centre Director Max Mayfield warned that New Orleans would be pounded throughout the day and that Katrina's potential 4.5-metre storm surge, down from a feared 8.4 metres, was still enough to cause extensive flooding.
"I'm not doing too good right now," Chris Robinson said via cellphone from his home east of the city's downtown.
"The water's rising pretty fast. I got a hammer and an axe and a crowbar, but I'm holding off on breaking through the roof until the last minute. Tell someone to come get me please. I want to live."
Along the Gulf Coast, the storm hurled boats onto land in Mississippi, lashed street lamps and flooded roads in Alabama, and swamped highway bridges and knocked out power to 28,000 people in the Florida Panhandle.
New Orleans, which was in particular peril because it is so low-lying, was ordered evacuated over the weekend, and an estimated 80% of its 480,000 residents complied.
Katrina is lashing New Orleans
with wind and rain
At the Superdome, home to 9000 storm refugees, wind peeled pieces of metal from the golden roof, leaving two holes that let water drip in.
People inside were moved out of the way.
Others stayed and watched as sheets of metal flapped and rumbled loudly. From the floor, looking up more than 19 storeys, there appeared to be openings of about six feet long.
Outside, one of the three-metre, concrete clock pylons set up around the Superdome blew over.
"The Superdome is not in any dangerous situation," Governor Kathleen Blanco said.
Scores of windows were blown out at some New Orleans hotels.
At the Windsor Court Hotel, guests were told to go into the interior hallways with blankets and pillows and to keep the doors closed to the rooms to avoid flying glass.
Katrina threatened more death
At 1100 GMT, Katrina was centered about 48km southeast of New Orleans.
That put the western eye wall with some of the fiercest weather over New Orleans.
The storm's winds dropped to 217kph as it pushed inland, threatening the Gulf Coast and the Tennessee Valley with as much as 38cm of rain over the next couple of days and up to 20cm in the drought-stricken Ohio Valley and eastern Great Lakes.
New Orleans has not taken a direct hit from a hurricane since Betsy in 1965, when a 2.4- to 3-metre storm surge submerged parts of the city.