The federal appliance rebates are finally here, but if you want yours, you’d better act fast.

According to the Wall Street Journal,  in Florida  the $17.6 million allocated for the program lasted a day and half, as more than 72,000 claims were filed. In Illinois, the second half of its $12.4 million, made available on Friday, April 16th disappeared in 11 hours.

Nationwide, $300 million in rebate money has been allocated by the federal government to 56 states and territories to encourage residents to buy furnaces, clothes washers, refrigerators and other appliances with the government’s Energy Star label. Typically, rebates run about $75 for a clothes washer and several hundred dollars for home heating and cooling systems.

But in an experience reminiscent of last year’s popular “cash for clunkers” program, which paid consumers to trade in gas-guzzling automobiles, interest in the appliance programs has been so been intense that the state programs are often running dry in a matter of days.

For example, Melissa Woodall, a single mother of three in Miami, said she began scanning appliance ads a few weeks ago for a new stove. She noticed an article about the rebates and decided to replace her old, leaky dishwasher and refrigerator.

The day before qualified purchases were allowed, she visited Sears to pick out the appliances. On Friday, she arrived to the store at 6:30 a.m. and found 49 customers in line. Fortunately, the store had given her a printout the night before. All she had to do was pay and arrange delivery, which still took an hour and a half in the crowded store.

And the ordeal was not over, Ms. Woodall said — she still had to get the rebate itself. At 11 a.m., when online signups began, she and her sister went to the state’s rebate site. “The Web site was flooded. It kept crashing,” she said. It took her an hour and 15 minutes to get registered for the rebate.

It was worth it, Ms. Woodall said. She paid about $1,500 for the dishwasher and fridge and will be getting about $500 back.

Each state has structured its own program, sometimes excluding certain appliances like air-conditioners or requiring proof that old appliances were recycled before paying out the cash. The amount of money available varies widely, from more than $35 million in California, where the program was scheduled to start on Thursday in connection with Earth Day, to $100,000 in American Samoa.

The federal government created the appliance rebate program as part of the 2009 stimulus legislation, and retailers say it has increased sales.

The high interest is understandable. The rebate programs come on top of existing discounts on Energy Star appliances, recycling and take-back rebates for old units, and specials provided by individual retailers. In some cases, consumers may qualify for federal or state tax credits, too.