Chairman Brian Colon said party rules allow the caucus to take until Feb. 15 to finalize and certify Tuesday's presidential preference vote, The Albuquerque Journal reported Friday.
At stake are 38 delegates. At one point, Sen. Hillary Clinton, D-N.Y., held a lead of less than 1,100 votes over Sen. Barack Obama, D-Ill, with several thousand provisional ballots uncounted, CBS reported.
Colon said he was "optimistic" the qualifying provisional process -- ensuring that those who cast them are eligible voters and didn't vote twice -- could begin.
"Over the next couple days, we'll have a good sense of exactly when we'll finish this process," Colon said. "If we need until the 15th, we're certainly going to take it. What's most important is that we're accurate, consistent and fair."
Colon and other state party officials have said higher-than-expected voter turnout swamped organizers Tuesday. Voters dealt with long lines and long waits many polling sites around the state. Some voters said they left without voting because of the delays, the newspaper said.