Miller's comments came during a Senate Finance Committee on the current tax filing season, which ends today for individuals.
Senate Finance Chairman Max Baucus (D-Mont.) appeared agnostic to Miller's request. But he pressed him to do more to stop offshore tax cheats.
"I urge you to be more aggressive," Baucus told Miller.
The Finance Committee does an annual review of IRS compliance.
Baucus intends to break that cycle by calling the IRS back to the witness table before April 15, 2011 so the agency can update him on its most recent effort to clamp down on tax cheats.