Your passport renewal or issuance will not be denied because you owe back taxes to the IRS. The IRS does not gives lists of delinquents to the State Department and there is no statutory provision that provides for a denial of your passport just because you have back taxes owed. If the IRS believes that you are about to leave the country and take assets with you, it has remedies available to it to seize those assets to pay your delinquent taxes. It also has a writ it can use to hold you in the U.S. until you pay, but this writ is rarely used due to the requirement needed to show the court to get it.
The only time I'd expect your passport to be jeopardy for federal taxes owed is if you have been indicted on federal tax evasion or fraud charges. In that case, the U.S. attorney may ask the court to require you to surrender your passport so that you can't leave until the criminal case is resolved.
So, go ahead and renew the passport.
I do suggest, however, that you get an installment agreement or make other arrangements with the IRS to pay what you owe. That can reduce the penalty that accrues on the unpaid taxes and will eliminate the need for you to worry about what the IRS might do.