Papen, D-Las Cruces, may have quietly assembled enough support to become president pro tem of the Senate.
It means that southern New Mexico, which only weeks ago appeared to be shut out of the Senate leadership, could yet have a lawmaker in a key job.
Papen lost to fellow Democrat Pete Campos at the party's caucus last month in the nomination process for president pro tem. But it is the full 42-member Senate that will elect the pro tem on Jan. 15, opening day of the legislative session.
Papen would win the job if she can pick up the votes of five of the 25 Democrats, plus all 17 Senate Republicans.
Papen has not responded to interview requests since she lost to Campos at the caucus.
But Sen. George Munoz, D-Gallup, a key swing vote, said Papen had continued her campaign and now was in excellent position.
"She is running, and I am voting for her. And, yes, I think she can win," Munoz said in an interview.
Munoz previously said he did not want to join a coalition in which a small group of Democrats would join with all Republicans to elect the president pro tem.
But, Munoz said, he had since decided that Papen was the best available choice.
The president pro tem has power in determining committee assignments for senators. Munoz said he would feel more comfortable with Papen in that role than Campos.
Campos, 58, of Las Vegas, said in an interview that he was seeking votes from senators of both parties.
"It's early. It would be premature to speculate on what can happen," he said.
But Republican Sen. Steve Neville of Aztec has said that his party's senators could support Papen, believing she would be fair to them. Papen decided to run for pro tem because she said senators of both parties encouraged her to seek the job.
In addition to Munoz, Papen appears to have locked up the votes of at least three Democrats her own and those of John Arthur Smith of Deming and Clemente Sanchez of Grants.
Smith, who wants to remain as chairman of the Senate Finance Committee, nominated Papen at the Democrats' caucus. Sanchez is a freshman lawmaker who works at the Grants campus of New Mexico State University.
The vote of one more Democrat would put Papen over the top, provided that all the Republicans support her.
But even with the votes of just four Democrats, Papen could have a path to victory.
Support from four Democrats and 17 Republicans would give Papen a 21-21 tie with Campos.
Sen. Howie Morales, D-Silver City, said Republican Lt. Gov. John Sanchez appears to have the authority to break such a tie, and he almost certainly would side with the Republican senators.
Sanchez is the presiding officer of the Senate, but his role generally is limited to recognizing senators during floor debate and keeping the proceedings orderly.
A tie vote in the Senate is the only time the lieutenant governor gets to vote on matters before the Senate.
Morales, citing attorney general opinions from 1959 and 1971, said the pro tem decision could end up in Sanchez's hands.
"Absent another opinion that I may have missed, or some other authority, I am concerned that the lieutenant governor does in fact have the authority to break a tie for pro tem," Morales said.
Morales is a southern New Mexico lawmaker who will vote for Campos.
Morales himself came close to winning the nomination for pro tem at the Democrats' caucus. He called for Democrats to support their top vote-getter. Given that stand, Morales said it would be inconsistent if he now backed Papen instead of Campos.
But Morales also said that a case could be made that Papen is more liberal than Campos.
Campos in 2009 voted with Republicans against conferring certain rights on same-sex couples. Papen supported the bill. It failed.
In 2011, Campos, a community college president, voted with Republicans to continue allowing spanking of students in public schools. Papen voted to outlaw it, and that ultimately is what happened.
Morales said the Senate could be a place of high drama on opening day. The possibility of a tie vote for pro tem looms, and early favorite Campos may not be able to hold off Papen's late charge.