The recently-installed metal detectors at the doors to the House chamber have become a flashpoint among some Republican members.
Trump adviser Jason Miller would not say whether others had signed on or whether South Carolina-based lawyer Butch Bowers would be the sole lawyer tasked with representing Trump.
John Catanzara, the president of Chicago's Fraternal Order of Police lodge, initially defended the mob that stormed the U.S. Capitol.
The two Republican senators' actions call for a probe and "a determination whether disciplinary action is warranted," the complaint said.
"The single most important thing the Biden administration needs to do to fight the pandemic is communicate honestly and openly with the American people about what needs to be done," one expert said.