The couple declined to give the contract price on their apartment, but according to the real estate Web site Streeteasy, one-bedrooms in the building have tended to sell over the past six months for $700,000 to $1 million.

A spokeswoman for One Brooklyn Bridge Park would not comment.

Mr. Vollono has a job in finance, and master’s degrees in public policy from Georgetown University and in business administration from Oxford University. Ms. Ortiz spent nearly a decade working at the State Department and now has a business importing French products. They have resources, experience with government, and even experience with the program, which Mr. Vollono used several years ago to buy a house in Newport, R.I. They are determined to make it work for them in Brooklyn, as well, so they can buy without a down payment and can keep the price they locked in months ago in a rising market. Yet the process drags on.

“The sad fact is that if you were the average young veteran,” Mr. Vollono said, “you’d give up.”

Mike Frueh, the director of the loan guarantee program, suggested in a phone interview that the primary reason the loans were rare in New York City was the cost of housing. He also pointed to a 2006 expansion of the program that allowed Veterans Affairs to guarantee loans in co-ops, which would make them more usable in New York City.

But he neglected to mention that the co-op inclusion expired at the end of 2011. During the period that the program had the authority to lend on co-ops, a spokeswoman said, it did not receive a single co-op application from anywhere in the country.

Representative Carolyn B. Maloney, a Democrat from the Upper East Side, introduced legislation last year that would permanently permit the participation of co-ops in the program. It would also require Veterans Affairs to promote that expansion, so that perhaps this time it might receive an application or two. Ms. Maloney said she planned to introduce the measure again during the current Congressional session.