Yes! The IRS's Offer in Compromise (OIC) program allows you to settle your tax debt for less than the full amount owed if you meet strict criteria.
The IRS accepts offers based on your "reasonable collection potential." Reasonable collection potential is equal to an amount they think they can actually collect from you given your income, expenses, and assets.
The process requires submitting detailed financial information and paying a $205 application fee (waived for low-income applicants). Despite the advertisements from tax relief companies that promise settlements for pennies on the dollar, the IRS actually accepts fewer than 40% of OIC applications.
The process can take a year or more so be patient and be prepared to provide updated financial information throughout the process.