GOP senators also accused Duncan of imposing an "unfunded mandate" on schools by asking them to take certain ObamaCare-related actions "without additional federal resources."
ObamaCare critics have increased their focus on the law's implementation in the last six months as the administration prepares for healthcare reform's most important provisions to take effect.
Republicans argue that federal implementation efforts should be limited to HHS.
The administration says that the rollout of major legislation tends to involve more than one department.
The senators asked for Duncan's reply by July 30.
Tuesday's letter was signed by Senate Republican Conference Chairman John Thune (S.D.), and Sens. Lamar Alexander (R-Tenn.), Kelly Ayotte (R-N.H.), John Barrasso (R-Wyo.), Roy Blunt (R-Mo.), John Boozman (R-Ark.), Richard Burr (R-N.C.) Saxby Chambliss (R-Ga.), John Cornyn (R-Texas), Ted Cruz (R-Texas), Deb Fischer (R-Neb.), John Hoeven (R-N.D.), James Inhofe (R-Okla.), Johnny Isakson (R-Ga.), Mike Johanns (R-Neb.), Ron Johnson (R-Wis.), Lisa Murkowski (R-Alaska), Pat Roberts (R-Kan.), and Jeff Sessions (R-Ala.).