The lawmaker also cast questions on whether the IRS should be trusted to implement key pieces of ObamaCare.
"Whether the IRS can be trusted to administer the tax laws while handling sensitive health insurance information is seriously in doubt. This growing trust deficit is alarming and should give all Americans pause," he said.
Thune is the latest lawmaker to join a growing bipartisan call for IRS employees to lose their jobs over the political targeting.
The IRS apologized last week for using words including "Tea Party" and "patriot" to identify conservative groups applying for tax exemption that should merit further scrutiny. While all Tea Party groups that had to answer additional questions as part of their applications ultimately received their exemptions, a report from the IRS watchdog found that insufficient oversight by management allowed the activity to go on for far too long, and needlessly delayed the processing of some of those applications.