At least 1.6 million Florida homes and businesses had lost power, according to Florida Power & Light and other utilities.
Earlier in the week, Irma sustained 185 mph winds for more than 24 hours, a record length of time for a hurricane in the Atlantic.
Irma, which killed at least 22 people as it tore through Caribbean islands toward Florida, has already claimed at least one life in the state.
The storm then headed for Florida's southwestern coast, making landfall again at 3:35 p.m. on Marco Island and weakening to a Category 2 shortly thereafter.
Antigua and Barbuda were spared from the worst of Jose, as it skirted north of the island on Saturday and was downgraded to a tropical storm warning. We checked historical maps dating back to the mid-1800s, and there was only one major hurricane that even comes close: a storm in the 1930s that crossed the Keys and traveled parallel to the state's west coast, but well offshore.
US President Donald Trump said his administration is monitoring the situation around the clock and is "as prepared as we can be".
Meanwhile, Scott acknowledged the fuel shortage that Irma had caused will likely continue, despite the state's efforts to ensure extra supply.
Palm trees blow in the wind in Naples, Florida, on September 10 as Hurricane Irma begins to hit Florida. The storm is expected to arrive in Tampa Monday by 2 a.m. EDT as a Category 3 with 115 miles per hour winds before heading to north western Florida by Monday afternoon with 85 miles per hour winds.
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"If Tampa stays on the east side of the eye, we expect the storm surge to be worse than if the eye moves inland and the west side of the storm hits it", he said.
Ports in Tampa and Miami - which, Scott said, are the primary ways fuel is transported to the state - were closed because of the storm. The wind was already picking up in St. Petersburg, some 400 miles north the Keys, and people began bracing for the onslaught.
The storm's path forced the largest evacuation in Miami-Dade County history and sent millions of Floridians fleeing. In streets carpeted with fresh green seaweed as the water receded, people said it was the strongest cyclone ever to hit the town.
In Miami-Dade, residents woke to the reality that they'd probably dodge the most unsafe part of the storm as its track shifted west. From there it will curve up into Alabama and Georgia on a westward turn.
The National Hurricane Center forecast that its center eye will move near or over the state's west coast later on Sunday.
"I will tell you in no uncertain terms - and I am not going to sugarcoat it - this is going to be a hard storm", Buckhorn said at the news conference.
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