Legal Question in Criminal Law in Texas

Yes, under some circumstances.

Not everyone is eligible for an appointed attorney. If you have the means to hire a lawyer, the court is not only allowed but expected to deny your request for appointed counsel.

Even indigent defendants are only entitled to a free lawyer when they risk being sent to jail or prison. If you're only facing a modest fine, you can be denied an appointed lawyer.

Further, it's up to you to prove that you can't afford to hire an attorney. If you refuse to prove this, your request will be denied regardless of how poor you might be.

Also, if you have been representing yourself and wait until close to trial before asking for a lawyer, the court may treat your request as a delaying tactic.

There are many other reasons why such a request could be denied.