Five of the 25 Democratic senators could enter the day as contenders for the leadership job.
They are Sens. Mary Kay Papen of Las Cruces, Howie Morales of Silver City, Carlos Cisneros of Questa, Pete Campos of Las Vegas and Linda Lopez of Albuquerque.
Papen, 80, said Democrats and Republicans had encouraged her to seek the Senate presidency.
But bipartisan efforts could work against her if Democrats decide to elect the president without any involvement from Republicans.
Republicans in the Senate number 17. They can be frozen out of the selection process for Senate president if at least 22 Democrats unite behind one candidate.
Morales, 39, is pushing for that to happen. Lopez and Cisneros also want a consensus candidate. Campos has been tight-lipped, saying in one interview only that he had an interest in the job.
The sitting president pro tem, Democrat Tim Jennings of Roswell, lost his bid for re-election to the Senate in this month's general election.
The president pro tem plays a key role in determining Senate committee assignments. In turn, committees decide whether bills advance to the full Senate or die.
An even more powerful job than Senate president is that of majority leader. That position is held by Sen. Michael Sanchez, D-Belen.
Sanchez, 62, said in an interview this month that he was comfortable as majority leader and wanted to continue in that role.
The majority leader can single-handedly kill a bill, as he decides which measures will receive a vote on the Senate floor.
Republican Gov. Susana Martinez used her political committees to try to defeat Sanchez in the general election. But he won with ease, and likely will continue as majority leader.
Milan Simonich, Santa Fe bureau chief of Texas-New Mexico Newspapers, can be reached at firstname.lastname@example.org or 505-820-6898. His blog is at nmcapitolreport.com