NEW YORK — The nation’s banks suddenly find themselves under pressure to throw greater lifelines to their most troubled mortgage borrowers. But don’t expect every struggling borrower to get a bailout.

Bank of America has already announced that it would forgive some of the principal for homeowners who owe more than their homes are worth. And the Obama administration will announce a plan today that would reduce the amount other struggling borrowers owe, two people briefed on the matter said.

The two people declined to be identified because the program had not yet been announced. But Herbert Allison, an assistant Treasury secretary, told reporters Thursday that officials are close to expanding the administration’s $75 billion foreclosure relief effort.

Government money will help many homeowners. But legal, logistical and financial obstacles may make it harder for banks to extend mortgage relief to the masses.

Allison cautioned that an extension of government aid is “not going to mean that all underwater mortgages are suddenly in the program.” A mortgage is underwater when it exceeds the value of the property.

Bank of America said Wednes- day it agreed to forgive a portion of the mortgage balances for some of its most troubled borrowers. The homeowners must have missed at least two months of payments and owe at least 20 percent more than their home is worth.

The details of the government’s announcement today were not immediately known. But its plan may be limited because of the amount of funds available and the complex structure of the mortgage business.

A big problem is that most of the troubled mortgages aren’t owned by the banks themselves. They were sliced and diced into securities during the housing boom and sold to investors. In order to reduce principal payments on those mortgages, banks often must get permission from the investors who holds the securities – who may not be willing to take less.

Banks can write down the principal on mortgages that they’re authorized to control. But for mortgages held by outside investors, they “really don’t have the power to overcome those legal obligations to the buyers of those securities,” banking analyst Nancy Bush said. “Their hands are tied.”

Making things more complicated are second mortgages, or so-called “piggyback loans.” Many lenders made such mortgages during the boom years, allowing consumers to make a small or no downpayment. Worrying that they won’t be repaid, lenders who extended second mortgages have been using their veto power to block borrowers’ efforts to modify their primary mortgages.

Bank of America spokesman Rick Simon said “a good portion” of the bank’s private investors have authorized the bank to modify the mortgages. He said, however, the principal reduction process gets more complicated when dealing with second mortgages owned by outside investors.

But part of the government’s relief program, which modifies second mortgages, could eliminate that hurdle. Citigroup Inc. on Thursday became the fourth large lender to commit to the program, part of the Obama administration’s $75 billion loan modification plan.