Here in USA, some debts to the government (such as certain school loans) can lead to a bad credit if the person defaults on the debt.
How is it with tax debt to IRS, can that lead to a bad credit?
I'm assuming by "bad credit" you mean low credit score or negative marks on your credit report. If so - yes, most definitely.
Not only that, the IRS can garnish your salary and put a lien on your property, and these also appear on the credit report and affect your credit score.