The International Union of Operating Engineers Local 953 did not recommend to its members they approve the contract, said Barry Dixon, president of the local.
The contract covers 450 surface miners at Navajo and San Juan mines west of Farmington. Underground miners at San Juan Mine are covered by a separate labor agreeement.
Voting began at 7:30 a.m. and will close at 7:30 p.m.
"It's probably going to be pretty late tonight before we know any result," Dixon said.
BHP gave the miners a "last, best and final offer" last Friday, Dixon said.
"We had a brief discussion on their proposal, and we told the company we couldn't recommend the proposal to our membership to accept," he said.
Dixon declined to describe BHP's offer, citing ongoing negotiations.
BHP Billiton is San Juan County's largest private employer. A statement from the company is expected later today.
The miners' current contract expires at midnight.
"If it passes, it's over and we go on our merry way," Dixon said. "If it's rejected, we go into an automatic 15-day extension during which we would most likely continue negotiating."
Navajo Mine is under pressure from a scheduled partial shutdown of Four Corners Power Plant, the mine's sole customer.
The decommissioning of three units would reduce demand for the mine's coal by about 30 percent.
The Navajo Nation has announced its intention to acquire the mine from BHP Billiton, an Australia-based mining company.
For more on this story, keep reading The Daily Times.