There is not a penalty for having income from a second job.   Your tax bracket depends on the total amount of your income, no matter what the source of the income was.  

@JM136 - the tax bracket is based on the sum of the two jobs..... but here is the issue I see when this occurs....many end up owing comes tax time.  Why?

Beacuse each employer withholds tax based on the federal tax tables not knowing about the other employer.  So the tax bracket ends up lower when looked at separately vs. adding the income together.  When you fill out the W-4 for the 2nd employer, suggest getting very conservative, Single and you may want to withhold extra each paycheck to mitigate the issue comes tax time. 

The IRS has a withholding calculator which makes it easier to get the answer than the 4 page W-4 worksheet : 

http://www.irs.gov/Individuals/IRS-Withholding-Calculator