Allied said it would decide today whether to proceed with the takeover effort.
The machinists represent about 20,000 workers at United and have played a central role in past takeover efforts.
Until yesterday, the board had opposed the takeover efforts of both groups.
The company is currently the target of a takeover effort by its own pilots' union.
Otherwise the takeover effort must be dropped for at least a year.
Analysts estimated the group's total costs, including three takeover efforts, at less than $14 a share.
But union and airline officials said several major obstacles would have to be overcome before a takeover effort could begin.
Interest soon died down after no sign of a takeover effort appeared.
Wall Street and the utility industry are also monitoring the takeover effort.
"His options became very limited," said a person close to the takeover effort.