I do not know how quickly Palm Beach County Judges are able to address evictions these days. However, under Florida Statute 83.59(2), an eviction is a summary proceeding (meaning it is a shorter process than a regular lawsuit) & the court is supposed to "advance" the case on its calendar, meaning the court is basically supposed to fast-track the matter, in the interest of restoring possession of the house to the landlord when the tenant has breached the lease.
Filing an Answer may prevent a default from being entered against you. However, under most circumstances you must pay all unpaid rent into the Court registry at the time your file your Answer or the landlord is still entitled to a default judgment & writ of possession to have you removed. You may wish to refer to FS 83.60 for further assistance. In general your situation falls under Chapter 83, Part II, Florida Statutes (ie, the FL Residential Landlord & Tenant Act).
This information is provided for general informational purposes only & does not create an attorney-client relationship with this author. It is strongly recommended that you seek the assistance & counsel of a local attorney who can provide you with detailed information based on your particular situation. Best of luck.