It all depends. First of do you want to tell your employer of your first job that you have a second job? There is no requirement to file a "new" W4 with your current or first employer regarding the income from your second job. Some employers are ok with an employee working a second job. Others it may be grounds for termination.
In your post you don't tell us about the two jobs or about yourself. If we assume that the first job is full time (40 hours a week) and the second job is part-time and earns less than the full time job. The question is will the new part time job raise your taxable income to the point that you are in a new tax bracket? Also, do you have a spouse that works?
Your best bet for taxes is to file the W4 as single or married with no dependents. The reason is that the second part time job will calculate withholding as if this is the only job. Depending on what you have withheld on your first job, the second job may not withhold any federal or state income tax. or not enough and you end up owing state or federal income tax when you file. By having zero dependents will cause withholding on the second job.
If you have too much taken out by both jobs you get a refund. If you have too little taken out you may owe taxes when you file. If you owe a significant amount you may also owe interest and penalties for both the state and federal returns.
Don't worry about FICA. If the two jobs put you over the max income for FICA you will get the excess as a refund or credit to amount due.
Again it all depends on your income situation. If your single and your first job you make $50,000 and the second part time job you make $10,000 filing your W4 as single with 1 dependent should work. If on the other hand you are married, you make $200,000 at the first job and your part time job you make $100,000 and you spouse woks making $200,000 with child credits and daycare you may want to talk to a tax expert to plan your tax strategy. But completing the w4 as single with no dependents might be your best bet. Think of it this way. Every additional dollar you make at the second job is taxed at your higher tax rate.
