Depends entirely on the circumstances. One or two counterfeit bills? Very plausible that they were passed to you and you're not guilty of anything other than bad luck.

50 or 100 counterfeit bills--very hard to explain away.

The State must prove that you knew that the money was counterfeit.

Besides the quantity of bills found on you, the circumstances of the possession and spending of the bills will also help determine what happens. For example, a government expert will likely testify that professional counterfeit passers will favor dark business like night clubs and bars for passing the currency. In addition, someone who breaks a $100 bill at one place and fifteen minutes is at another place breaking another bill will be highly suspect.  On the other hand, spending the bills at a place where they know you is good evidence that you did NOT know. Being able to tell police exactly who gave you the counterfeit bills will also help. If you keep silent about it, that tells another story.