Lt. Gov. Michelle Fischbach said on her first day on the job that she would reject a salary for the position and remain a Republican state senator.

“My primary focus will continue to be serving the citizens of Senate District 13 in the Minnesota Senate, who elected me to a four-year term,” Fischbach said in a statement Wednesday.

DFL Senate Minority Leader Tom Bakk flatly rejected Fischbach’s claim on both offices: “Congratulations on becoming lieutenant governor of the State of Minnesota,” he wrote in a letter to Fischbach Wednesday. “As you know, the Minnesota Constitution prohibits you from simultaneously holding the offices of state senator and lieutenant governor.”

Fischbach’s move is just the next step in a surprising turn of events that began with the resignation of former U.S. Sen. Al Franken and could wind up with a special election to replace Fischbach in the Senate, with control of the chamber on the line.

And, Fischbach would run to reclaim her own seat.

Fischbach ascended to her new role following Gov. Mark Dayton’s appointment of former Lt. Gov. Tina Smith to the U.S. Senate; she was sworn in Wednesday. As president of the Minnesota Senate, Fischbach automatically became lieutenant governor as called for in the state Constitution.

DFL Senate Minority Leader Tom Bakk flatly rejected Fischbach’s claim on both offices.

By trying to remain in the Senate, Fischbach, a Republican, is helping her party maintain its narrow majority status.

Currently, if Fischbach keeps her Senate seat, Republicans will control the upper chamber by 34-32. If the DFL wins a special election to replace former Sen. Dan Schoen, then the Senate would be 34-33.

DFLers say the Minnesota Constitution forbids Fischbach from holding two offices at the same time and plan to sue to remove her from the Senate. If they win in court, the Senate would be an even 33-33, with a special election to replace Fischbach.

In the event of that, Fischbach said she would run for her Senate seat and resign as lieutenant governor if she is elected. The annual salary for lieutenant governor is $82,959.

Adding to the quirkiness: Fischbach is now serving in Dayton’s DFL administration: “The position of lieutenant governor has no constitutional duties and its authority is what is provided by the governor. I have had cordial conversations with Gov. Dayton and am looking forward to a positive relationship with him and his staff,” she said in the statement. Fischbach also said she would decline the lieutenant governor’s larger salary.