After churning through the Caribbean and chugging up the Gulf of Mexico, Hurricane Isaac made landfall over southeastern Louisiana on Tuesday night -- bringing with it sustained winds of 80 mph and torrential, stinging rains.

According to the National Hurricane Center, the storm's center moved over land in Plaquemines Parish at 6:45 p.m. (7:45 p.m. ET) -- one day before the seventh anniversary of Hurricane Katrina, which left nearly 1,800 dead and caused billions of dollars worth of damage along the Gulf Coast.

Isaac's eye then "wobbled westward" and moved back over Gulf waters, and by 10 p.m. CT was centered about 75 miles southeast of Houma, Louisiana -- all while keeping its strength as it lashed those onshore.

Throughout the night, the hurricane center issued advisories indicating that steady hurricane-force winds of 74 mph and stronger were being felt 60 miles out, mostly to the east and northeast of Isaac's eye. Sporadic gusts were even stronger, including a 106 mph wind reading from high up on an oil rig off the southeast Louisiana coast and 85 mph in Grand Isle, Louisiana.

While Isaac is expected to eventually lose steam, that might not happen immediately because much of the sprawling storm will be over water for several more hours.

Even with more dangerous conditions likely yet to come, the storm already has caused significant surges and flooding in a number of locales, and not just those directly in Isaac's path. Storm surges of 10.3 feet have been reported in Shell Beach just outside New Orleans, and 6.7 feet in Waveland, Mississippi, according to the hurricane center.

These surges likely will get worse, with forecasters predicting water levels to rise between 6 to 12 feet on the coast in Mississippi and southeastern Louisiana alone.

Mississippi state authorities have noted that waters have gone up around the state faster than expected, something Jim Yelverton noticed as he surveyed the Tchoutacabouffa River in Biloxi. He estimated Tuesday afternoon that this river was 6 to 8 feet higher than normal, and at low tide, expressing concerns about even more flooding during high tide Wednesday morning.

"The fact that we haven't had any rain and that we've got six to eight hours before the real fun begins ... makes me nervous," echoed Jon McDougal, another CNN iReporter who documented flooding in nearby Gulfport.

A large swath of the northern Gulf Coast on Tuesday night was experiencing tropical storm conditions, with winds in excess of 39 mph, including parts of Mississippi and Alabama, the hurricane center reported.

Intense rains alone could cause major headaches, and flooding, given Isaac's slow progression.

Having at one point swept through the Caribbean at 21 mph, Isaac's movement slowed Tuesday to 8 mph. It continued creeping northwest at this speed through Tuesday night.

Because Isaac is moving at such a slow clip, CNN meteorologist Chad Myers estimated some residents could experience hurricane or tropical storm conditions for between 24 and 36 hours before the storm finally moves on.

While residents had been feeling its effects for hours, the storm's eye was still 75 miles south-southeast of New Orleans at 10 p.m. Tuesday.

By then, heavy rain had already contributed to significant flooding, including "deceptively deep" water under Interstate 610 at Elysian Fields. But due to the strong winds, barriers aimed at keeping drivers away flailed in the wind.

"Please help us spread word: I610 Underpass at Elysian Fields is flooded. We cannot keep up barricades b/c of wind. Do NOT try to cross," the city said via Twitter.

Mayor Mitch Landrieu said he expected the worst of the storm to hit his city Wednesday morning, bringing with it hurricane-force winds and between 10 and 16 inches of rain. The mayor wrote on Twitter that about 1,000 National Guard troops and more than 2,900 law enforcement officers are in the city ready to address issues related to the storm.

"We're in a hunker down phase now, because this storm could be over us for a while with a lot of wind and rain," Landrieu said in a statement. "Hunker down means hunker down and prepare to ride it out."

Like Landrieu and other local and state authorities, President Barack Obama on Tuesday had urged those in Isaac's path to listen to authorities and stay safe.

"Now's not the time to tempt fate," he said from Washington, after signing an emergency declaration for the state of Mississippi like he had for Louisiana a day earlier. "Now's not the time to dismiss official warnings. You need to take this seriously."

Besides strong winds, Isaac could bring 14 inches of total rainfall in many places, and isolated parts of southeast Louisiana, southern Mississippi, southern Alabama and the Florida Panhandle could get as much as 20 inches, the hurricane center said.

Entering Tuesday, Gulf Coast residents braced for the worst from a storm that has already caused considerable devastation as it headed north from the Caribbean. Haiti's civil protection agency reported at least 19 people in that country died due to Isaac, which after hitting that impoverished nation went on to lash Cuba and the Florida Keys.

Trish Powers, a CNN iReporter from Fort Pierce on Florida's east coast, reported that floodwater there is "almost waist deep at some ... points."

"All we can do is wait for the water to recede," she said.

The hurricane's "increasing winds and seas" disrupted a search for a missing man on Tuesday, Coast Guard spokesman Timothy Williams said.