Amy Harrington is sitting on a carpeted floor facing a mirror, cradling 5-year-old Molly Muzzillo in her lap. Molly's long auburn hair sways as Harrington rocks the little girl from side to side.

''Rock, rock, rock the boat, gently down the stream,'' Harrington sings, and Molly sits, transfixed, looking in the mirror. Harrington, a speech therapist, draws her curled fingertips together, then separates them, making the sign-language symbol for the word ``more.''

''Are you going to ask for more?'' Harrington asks, encouraging Molly to sign the word. She waits, and waits, but Molly does not ask for more.

Stricken at birth with a rare genetic disorder that has left her physically and mentally disabled, it's profoundly difficult for Molly to express herself, to say even a word as simple as ''more.'' Her parents, Laura and Steve Muzzillo of Cooper City, speak for her.

For two years, they have been asking for more. But they are among 10,500 Floridians on a waiting list for services for disabled people.

INCREASED DEMAND

In four years, Gov. Jeb Bush has doubled funding for the state program, which is designed to allow even severely disabled people to avoid living in institutions. But the number of Floridians served by the program has tripled. Meanwhile, thousands more have asked for help and have been turned away.

This year, Bush is asking for between $80 million and $100 million in new spending. Advocates for the disabled say it will barely keep pace with new demand and other strains on the system, such as the needs of current clients.

Because Molly Muzzillo's disorder is congenital, the Muzzillos repeatedly have been denied private insurance. In October, the state canceled the family's Medicaid coverage for Molly, saying Steve's salary of about $50,000 left him ineligible for that federal program, which covers only the most financially needy.

The state's earlier decision to grant coverage was a mistake, the Muzzillos say they were told.

With the Medicaid coverage, the Muzzillos qualified for nine hours of speech, occupational and physical therapy each week. Now, they can afford no more than one hour of speech, and therapists say Molly's progress already has diminished.

LONG WAITING LIST

Molly would almost certainly be eligible for the state program, which uses state and federal dollars to offer care and insurance to disabled people regardless of income. But for every three Floridians who are on the plan, another one is on the waiting list.

''I've done everything they've told me to do, and they just keep saying no. I don't know what else to do,'' said Steve Muzzillo, who owns a Pembroke Pines medical supply store with his brother.

''I try so hard to get what she needs, and I'm failing as her father,'' Muzzillo said, his eyes welling.

The problem isn't a new one. In 1996, when U.S. District Judge Wilkie Ferguson said the state was breaking the law by requiring Floridians to wait years for taxpayer-funded care, the state was ranked 47th in the nation in the amount it paid to help the disabled.

Bush's first budgets set aside $360 million in new dollars to allow the disabled to live in their own homes, or small group homes, while receiving the care they needed.

IMPROVED RECORD

Within about two years, the state's waiting list, with between 9,000 and 10,000 names, was eliminated, and perhaps another 5,000 to 6,000 Floridians began to receive services under the Medicaid

program. Now, 25,000 Floridians are receiving some type of help.

Florida moved up to 37th in a report published by University of Colorado Professor David Braddock.

But as administrators with the Department of Children & Families struggled to eradicate the waiting list, a new one developed. And now it's longer than the one that Bush inherited, with about 10,500 names.

In Braddock's most recent report, which uses 2000 figures, Florida had slipped back down to 48th in the United States for the money it invests in care for the disabled.

Most people on the waiting list could begin to receive care immediately, if they opted to live in either a public or private institution, mostly large facilities where profoundly disabled people live in campuslike settings. A bed in such an institution costs, on average, about $75,000 per year.

ONE-THIRD AS MUCH

But for those on the waiting list, the state will not pay one-third of the cost to allow a disabled person to live in his or her own home.

''Here, I'm looking for $1,500 a month just to pay for her therapies,'' Steve Muzzillo said. ``And yet they will pay $70,000 to put her in an institution.''

Elizabeth Hirst, a spokeswoman for Bush, said his administration must be credited with doubling the dollars that pay for community care for the disabled.

''It has very much been his priority to improve the quality of life and the services provided to our citizens who have developmental disabilities,'' she said. ``Right now, what we're looking at are more disabled persons receiving services who never have before.

''The governor wants to do more,'' she said. ``This is one of the few areas in which he is calling for increased funding.''

A spokesman for the Department of Children & Families, which mostly administers the program, could not be reached for comment.

Helene Good, who heads the Miami-Dade-based Community Committee for Developmental Handicaps, said state officials grossly miscalculated the number of disabled Floridians who needed help.

IMPOSSIBLE WAITS

For decades before Ferguson's 1996 ruling, many disabled people were told not to bother putting their names on a waiting list. In some counties, it was not uncommon to wait 20 years before some help was offered.

''There was a whole generation of people who didn't get services,'' Good said. ``When money became available and people were able to begin receiving services, we had a whole generation of people who had been waiting, plus everyone else who had been born or moved to the state.

''No matter how much of an increase you put into the program, which has been considerable, there was no way it would be enough to address essentially 25 to 30 years of financial neglect,'' Good added.

Maritza Ruiz believes the plight of her cousin could not be much more urgent. Ruiz's 38-year-old cousin, who is on the waiting list, is profoundly disabled -- incapable of walking, eating or bathing without assistance. Her elderly mother has grown frail and infirm caring for Ruiz's cousin and now suffers from diabetes, high blood pressure and a ruptured disk.

EXTREMELY WEAK

Still, Ruiz's aunt waits. She cannot lift more than five pounds and has to have groceries delivered because she cannot leave her daughter alone.

''She really, truly needs help, and she has never abused the system before,'' Ruiz said. ``For her, she says, the best scenario will be that they both die together.

''You have to be out on the street and homeless before you will get care,'' Ruiz said, ``which is outrageous.''

For some, even the prospect of losing a home is not enough. Denise Karp and her husband, Marc, also on the waiting list, took out a second mortgage and refinanced their Coral Springs home to pay for expensive therapies for their autistic 8-year-old son, Noah. With Marc Karp's cosmetic display business failing, the family has been unable to make payments on the mortgage in more than a year.

In recent months, the Karps have seen their phone service cut off and threats to turn off the electricity.

Nevertheless, Denise Karp regrets nothing. Thanks in part to the intensive therapies, language tutoring and behavioral programs, Noah can speak and read now.

''I could not stand by and let my child wither,'' she said.

NOT LIKE OTHERS

Molly Muzzillo was 17 months old when the Muzzillos learned their perfect baby was not perfect. Molly could not speak, walk or do many of the other things that other toddlers could do. They took her to a specialist, who proclaimed, ``Do whatever you can for this child, because she will never be normal.''

Over time, grief gave way to determination, and the Muzzillos set about doing everything they could to make Molly as ''normal'' as possible.

Molly attends a preschool run by the Ann Storck Center, a Broward County agency that cares for disabled children and adults. She plays with her Bijon Frise dog, Spunky. When her parents can afford it, they take her horseback riding, because experts say it may help prompt her to talk.

LOSING PROGRESS

But Harrington, Molly's speech therapist, said the little girl already has shown disturbing signs of losing progress since the family cut back on her therapies.

Early-childhood-development experts say small children suffer the most from a lack of services.

''If an adult has a stroke, you do not wait five years and then give them therapy,'' said Adele Luxa, an occupational therapist at St. Petersburg's All Children's Hospital, which serves children throughout Central Florida. ``That doesn't make any sense. The closest to the injury, whether it is a birth injury or congenital, the more impact you have.''