Some radio and TV stations have reportedly been knocked off the air at least temporarily. In Marathon, according to CBS Station WFOR-TV, power outages are a problem in some parts of the city.
Wilma strenghtened steadily overnight as it headed toward land, spawning at least three twisters and, off the coast of the Florida Keys - a water spout.
National Hurricane Center Director Max Mayfield has warned that the storm surge in the area south of Marco Island could reach 17 feet.
"This is a very dangerous hurricane," said Mayfield. "People need to stay hunkered down."
Hurricane Wilma's strongest winds began lashing southwest Florida early Monday, battering the coast with torrential rain and pounding waves that threatened flooding in low-lying areas.
The outer eyewall - the ring of 125 mph winds surrounding Wilma's calm eye - is buffeting land in the area where landfall was expected later, likely near Naples and Marco Island.
Wilma, a powerful Category 3 system, got stronger as it neared Florida. The storm's maximum sustained winds were measured at 125 mph - up 10 mph from late Sunday night. A 17-foot storm surge is possible along the southwest coast.
More than 22,600 people are in shelters across the state. But in the low-lying Florida Keys, not even 10 percent of the Keys' 78,000 residents evacuated, Sheriff Richard Roth said.
"We were born and raised with storms, so we never leave," one holdout, Ann Ferguson, explained from her front porch in Key West on Sunday. "What happens, happens. If you believe in the Lord, you don't have no fear."
That could prove to be a mistake: While Wilma is not expected to make landfall over the Keys, the storm could bring a surge of 8 feet to sections of the low-lying island chain.
"They're going to be in deep trouble," warned Billy Wagner, the senior Monroe County emergency management director. Key West was already experiencing minor street flooding early Monday and a wind gust of 76 mph was measured there. Power outages were reported in both the Keys and along the southwest side of the state.
Hurricane-force winds of at least 74 mph extended 90 miles from the center and wind blowing at tropical storm-force reached outward 230 miles, the hurricane center said.
In Miami Lakes, as Wilma spun more than 150 miles away, the blue glow of transformers exploding illuminated the pre-dawn sky. Large signs marking exits on the Palmetto Expressway were already toppled by Wilma's gusts - which were only a tropical storm force at that time.
Wilma's imminent arrival also was announced by at least four tornadoes - including one near Kennedy Space Center at Cape Canaveral - that caused some structural damage, but no injuries.