Yes - most private attorneys do some pro bono work in the right situation.
However, you are probably better off with a public defender (which you're entitled to if you cannot afford an attorney) than an attorney that's willing to take this case for very little or no money. The public defender is there for this very reason - a person in need of a defense attorney on a criminal case, but who cannot afford to hire on on their own. There are some excellent attorneys in the public defender's office. Rather than ask for somebody to give you a cut rate on their fees and not put 100% into your case, stick with the public defender, because as they say, "Good attorneys aren't cheap and cheap attorneys aren't good."