Can POTUS Sue Congress when they clearly neglect their duties?

[Yo_Mama]

18. Back when a Democratic Senate was refusing to vote on Bush appointees,

Biden was not so concerned:
https://en.wikipedia.org/wiki/George_W._Bush_judicial_appointment_controversies

People have short memories:

Yale law professor Bruce Ackerman wrote an article in the February 2001 edition of the magazine The American Prospect that encouraged the use of the filibuster to stop Bush from placing any nominee on the Supreme Court during his first term.[3] In addition, law professors Cass Sunstein (University of Chicago) and Laurence Tribe (Harvard), along with Marcia Greenberger of the National Women's Law Center, counseled Senate Democrats in April 2001 "to scrutinize judicial nominees more closely than ever." Specifically, they said, "there was no obligation to confirm someone just because they are scholarly or erudite." [4]

On May 9, 2001, President Bush announced his first eleven court of appeals nominees in a special White House ceremony.[5] This initial group of nominees included Roger Gregory, a Clinton recess-appointed judge to the Fourth Circuit, as a peace offering to Senate Democrats. There was, however, immediate concern expressed by Senate Democrats and liberal groups like the Alliance for Justice.[6][7] Democratic Senator Charles E. Schumer of New York said that the White House was "trying to create the most ideological bench in the history of the nation."[8]

As a result, from June 2001 to January 2003, when the Senate in the 107th Congress was controlled by the Democrats, many conservative appellate nominees were stalled in the Senate Judiciary Committee and never given hearings or committee votes.[9]

I don't think that tactic worked well for the Dems, and I don't think the Republican-controlled Senate now should refuse to vote on Garland. But nothing could possibly stop them from going through the process slowly and then rejecting him, thus achieving the same result.