The short answer
Usually yes if the person is your employee, and the rules turn on your state and how you classify them rather than on how long the job lasts. One day of work is still work, and an injury on day one costs the same as an injury on day one hundred.
Why the length of the job does not decide it
Most state workers compensation rules are written around the employment relationship, not the calendar. A worker you direct, supervise, and pay by the hour generally looks like an employee whether the job runs one day or one month, and the coverage requirement follows that relationship.
So the question is never how long the job is. It is whether this person is your employee, and whether your state requires coverage for employees like them.
Where the state lines fall
Every state sets its own rule, and the differences are real. Some require coverage from the first employee. Some start at three, four, or five. A few let employers opt out entirely, and a couple treat construction work more strictly than everything else.
Search your state name plus workers compensation requirements and read the state's own page, the one ending in .gov. It takes five minutes and it is the only version of this answer that applies to you.
What it costs to skip it when you needed it
The penalties are not small. States charge fines per day uninsured, and many add a stop work order that shuts the job down until you are covered.
The bigger number is the injury itself. With no coverage, the medical bills and the lost wages land on you personally, and in many states the worker also gets the right to sue you directly, which coverage would normally have taken away.
Homeowners are a different situation
If you are a homeowner hiring somebody for a Saturday, you are usually not the same as a business hiring a crew, and some states exempt casual or domestic work.
Your homeowners policy may include a small amount of medical payments coverage for someone hurt on your property, and it may exclude anybody doing paid work there. Those are two different clauses and only your policy says which you have.
One phone call answers it. Ask your agent: if I pay somebody to help me at my house for a day and they are hurt, what does my policy do?
If you hire through a contractor instead
When you hire a licensed contractor who brings their own crew, their coverage should be the one that responds. Ask for a certificate of insurance before the work starts.
A certificate shows the policy exists, who it covers, and when it expires. It is a snapshot, not a guarantee, so look at the dates and make sure the name on it is the company actually doing your work.
What to do before the crew shows up
Read your state rule, call your agent, and decide which side of the line you are on before anybody is on your site.
If you hire regularly, a policy is not as expensive as most people expect, and it is priced off your payroll. Compared to one back injury with no coverage, it is not close.
This guide is general information, not legal, tax, or insurance advice. Rules differ by state and by situation, so talk to your own professional before you rely on it.