New York City ? 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 today a plan that will expand the administration’s $75 billion foreclosure relief effort by reducing the amount other struggling borrowers owe.

The changes “will better assist responsible homeowners who have been affected by the economic crisis through no fault of their own,” an administration official said.

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.

Herbert Allison, an assistant Treasury secretary, cautioned Thursday 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 it is tied to.