W4 for maximing Roth 401(k) in a side job

I'm starting a side job that comes with a W2 and a 401(k) plan. I don't expect much income from this job, maybe $2000 over the full year, and I'd like to put as much of that income as possible into a Roth 401(k).

First thing make sure that you are eligible for the 401(k) plan. Some companies don't let part-time employees put money into the plan. If they do they might not match for contributions. Some companies will let new employees participate, others won't unless you work 1000 hours in the last 12 months.

If the paychecks are fairly uniform in gross pay, you may end up with very little federal and state taxes withheld because the tax tables would see this as a job that would only pay you around $2,000 a year, which is well below the federal standard deduction.

If they treat this pay as not a regular paycheck, they might tax you at the 22% rate. They would essentially be treating this as a bonus check. You might find that checks done this way don't allow you to contribute to the 401(k). I don't know that they can treat this like a bonus check, but I wanted to mention it.

Regular checks would also have social security and medicare withheld.

When asking about your eligibility for the 401(k) ask what the maximum percentage you can have withheld from your paycheck. Many (most?) companies won't let you have 100% sent to the 401(k). They will limit you to something like 85%. That is because they will have to collect social security and medicare, and if you were paying for health insurance that would also be done before any money was sent to the 401(k).

This $2000 income would come with $X of tax liability (which I won't know for sure until the end of the year).

Yes that is true. The $2,000 will be taxed at your highest bracket, but as discussed earlier you may have very little withheld for taxes from those checks if they are spread across many paychecks.

Is it OK for me to put all $2000 in the Roth 401(k), and then cover the $X in tax as part of my estimated taxes?

Yes, you would have to do this even if you weren't going to put money into the 401(k).

Or is the maximum I can put into the Roth IRA $2000-X, in which case I need to fill in the W-4 as accurately as possible now?

How they pay you will determine if anything is withheld. You could fill-out the w-4 with a large value in line 4(b) because you were expecting to have a large amount to itemize. But I think it won't make much difference, unless all your pay only applied to 2 or 3 checks.