As a New York attorney, I cannot advise you as to Florida state laws or procedures, but can make certain observations that may be helpful to you. While landlords have a right to receive rent and can bring eviction proceedings when rent is not received, courts in landlord/tenant proceedings quite often will permit extensions of time to either pay arrears or to move out if certain circumstances are present that complicate the matter. Thus, for example, you would expect a very elderly person or a disabled person to be provided with certain accommodations as to time.
If you are not represented by an attorney, you should at the next court appearance acquaint the court with any circumstances that affect you that may hamper your ability to rapidly move, such as children or impoverishment. You would probably do well to contact a local attorney and ask what options are available to you.
The New York attorneys answer is wrong. County courts in Florida routinely evict families with small children. Whether the judge will extend the time for moving depends on the individual judge, and the extension may be 1 or 2 weeks. Three months is highly unlikely. The tenant can be evicted in a very short time frame if the tenant does not know their rights. The tenant should speak with an attorney that has experience representing tenants in Florida courts.