OMB, acting through OIRA, has a wide range of mechanisms to manage federal agencies. None of these mechanisms can approach the reach of the Paperwork Reduction Act (PRA). Consider that the PRA:
(1) prohibits any federal agency from imposing any reporting or recordkeeping requirement on ten or more members of the public without an approval by OMB,
(2) is the only substantive control OMB has over independent agencies,
(3) states that OMB approval of the aforementioned reporting and recordkeeping requirements are not judicially reviewable and must comply with the Data quality Act,
(4) is self-enforcing since OMB must assign a control number to each reporting and recordkeeping requirement and no member of the public has to furnish any of the said information without an OMB control number and,
(5) states that no member of the public can be prosecuted for failure to furnish any information to a federal agency if the said agency does not have a control number.
See this recent action by OIRA based upon the PRA.
See this post for a history of the PRA.