The Northeast Corridor carried 11.4 million passengers last year, about 36 percent of Amtrak's total national ridership of 31.6 million.
Boardman said that the Northeast Corridor is in dire need of a major overhaul, and that without a significant increase in capital funding, Amtrak is "vulnerable to a bigger, costlier, and far more damaging failure than anything we have seen."
"The nation cannot afford to let a railroad that carries half of Amtrak's trains and 80 percent of the nation's rail commuters fall apart; the economic consequences would be devastating," Boardman wrote.
Amtrak is seeking $1.62 billion in federal funding for operating and capital costs nationwide in fiscal 2015, an increase of 16 percent from this year's federal appropriations.
And Amtrak is expected to ask for about $2.5 billion the next year, driven by a doubling of the costs of construction projects in the Northeast Corridor, according to the congressional letter.
The heavily used corridor, with its century-old bridges and outdated equipment, cannot be maintained "at today's financing levels or with today's policy instruments," Boardman said.
He urged Congress to give Amtrak multiyear capital funding guarantees, instead of annual appropriations that limit the railroad's ability to carry out expensive improvements.
"Only this type of commitment will allow us to plan and undertake major multiyear projects like bridge and tunnel replacements," Boardman wrote in his letter to House Speaker John Boehner and Senate President Joseph Biden Jr.