I just did my taxes for this year and it appears that instead of getting a refund, I owe the federal and state governments about $200 each. Is this normal? I thought employers set the withholding so that you end up overpaying and you get a refund at the end of the year. I'm trying to talk to the payroll department but they are quite unhelpful. :-/ What I'm worried about is that I might be doing something wrong in my tax return. I used two popular tax calculation software and they both give about the same numbers due.

'I thought employers set the withholding so that you end up overpaying and you get a refund at the end of the year.' Nope. That's your job.
What isn't normal is owing the state as much as the feds.
We can't know if you are using the software correctly or not. Did it ask for your J-1 status? Or if your employer put numbers in the wrong boxes. Or if you are entering numbers incorrectly.
Take it all to a tax place for a quick look.

(PS - I never in my wages life set mine up to overpay! Why should the IRS have my money interest free?
Set it up to pay as little as possible.)

As Joy said, it is up to you, not your employer. When you were hired you were given a W4 form. These forms are used to set your exemptions to determine your withholding. Set them too high and you are under withheld and owe money. Set them too low and you are over withheld so you get a refund. But it also means you are loaning Uncel Same money, interest free.

Thank you for your reply, none of the softwares I used ask for my J1 status.

You are considered a Nonresident Alien for the first 2 (non-student) years or 5 (student) years, and file a 1040NR.

Turbo Tax doesn't support that as far as I know. Maybe none of them.

The good news is that maybe you don't owe anything.

Right, that's why I could not use any software for the last two years. This year I am a resident alien.

You didn't tell us that.
Oh, on another question?
It helps us if you keep them together under one thread.

Sorry, I forgot to mention that I am a resident alien now.

Does this mean that the tax software is likely to be correct?

Yes, the tax software IS likely correct.

And paying is NOT a bad thing; REFUNDS are, because you are getting back your own money that you lent the government for the past year interest-free.

I'd like to owe a small amount every year. You have used their money all year!

The place you work does not "set" how much is withheld. You choose how much by the number of withholdings and if you wish any additional withheld. The place you work just does what you instruct them to do.

Remember any money back (refund) is just your money they kept at no interest during the year.