Among the tax breaks at risk in the negotiations between the White House and Congress to avert the “fiscal cliff” is a measure aimed at helping struggling homeowners.

Since the housing market collapsed, banks have been pushed to extend mortgage relief to struggling homeowners. But those households could soon receive an extra tax bill if Congress does not extend a five-year tax break.

The mortgage relief is aimed at some of the hardest hit: those who are underwater on their mortgages, owing more than their homes are worth.

Since 2008, more than 800,000 homeowners have been allowed to sell their homes for less than they were worth, known as a short sale, through a government program. In other cases, banks have lowered the balance owed on mortgages to make the payments more affordable and to encourage homeowners not to walk away. Both types of mortgage relief were key to a $25 billion mortgage settlement between the government and big banks this year.

But these programs could turn into a hefty tax bill for some.

‘Fiscal cliff’ calculator’: What it will mean for me

In a short sale, the difference between what is owed on a mortgage and the price at which a homeowner is allowed to sell his or her home could be considered taxable income. The same is true when the principal balance of a mortgage is reduced.

That tax liability was waived under the Mortgage Forgiveness Debt Relief Act of 2007, which expires at the end of this month.

Housing advocates say the loss of the tax break would not be fair to financially strapped homeowners who are hardly in a position to pay.

“You’re playing with people’s economic lives,” said Marceline White, executive director of the Maryland Consumer Rights Coalition.

Extending the tax break has bipartisan support in the House and Senate, Sen. Debbie Stabenow (D-Mich.) said. But it is included in a package of legislation related to the “fiscal cliff,” a series of tax increases and spending cuts set to take effect Jan. 1 that threatens to push the economy into another recession.

“One way or another, we need to get this done by the end of the year,” said Stabenow, who is pushing to have the tax break extended through at least 2014.