Generally, you should try to plan your project 2 months in advance, sometimes longer.
Availability for painting contractors will vary depending on the time of the year and the quality of the contractors work.
Just like people don't like living paycheck to paycheck, contractors don't like living job to job so we schedule out enough time to where we have a good cushion of work and it's still convenient for the homeowner.
The size of the project can also determine how soon the painting contractor can get to it.
The probability of getting on the schedule for a small job is greater than a large one because of things like:
Finishing a job earlier than expected, which may leave a day or 2 open between jobs.
Rainy day schedule - if your painter does exterior work, an interior job can be scheduled for a day when rain will occur. (Downside is that you will need to be available on short notice.)
In the past week I've had 4 estimate requests that ended on the phone because they wanted them done before my schedule allowed.
Avoid this with good planning. It will also allow you to adjust your budget if it happens to cost more than you anticipated.
Contractor tip: Plan for interior painting during the winter time when schedules are flexible and more openings may be available.