What is withheld for social security has no bearing on a refund or balance due.
This happens frequently with married couples who by themselves are taxed at a lower rate but are pushed into a higher rate with the second income. Make sure you both have zero on your W-4 at work and you may have to ask for an additional amount to be withheld over and above that. The exemption you put on your individual W-4 tells your employer how much to withhold based on weekly or bi-weekly income. The table can't possibly take into account that there is a second income and together all the income is taxed at a higher rate.
