Barr faces criticism over his actions, which Democrats say have politicised the Justice Department to support Trump.
The postponements mark a potentially ominous development for professional sports leagues in the US and Canada.
The US Supreme Court earlier rejected Trump's argument that he was immune from state criminal probes while in office.
Federal agents face accusations of excessive force as they operate in Portland against the wishes of local authorities.
Republican measure would include additional direct payments to Americans, as well as liability protection for business.
