The two sides have angrily blamed each other for the failure to agree on labor savings.
He said that the agreement would provide about $450 million in labor savings over the next four years.
"This $600 million will be included in your agency's executive budget if the labor savings are not agreed to by April 1," the letter says.
One issue mitigating against this drive for labor savings is government regulation.
United Airlines did not immediately address the amount of labor savings proposed by the unions.
The labor savings are certainly perceptible, if not exactly enormous.
You may have to mow more often, but the labor savings come in not having to bag the clippings.
The labor savings are expected to exceed $5 billion over six years.
But the new offer still calls for $450 million in labor savings over the next four years.
The plan calls for obtaining the labor savings or, failing that, laying off enough workers to balance the budget each year.