The variables which affect how much is withheld are (1) number of allowances; (2) single or married; and (3) optional additional amount withheld. Of course, your salary affects it also.
What your question to payroll should be is "Can I specify the exact dollar amount being withheld from my check for federal taxes, or do I need to figure out what number of allowances filing single (or married, if you'd like) will work out to that amount?" If it's the latter, then ask them what the right number of allowances is.