WASHINGTON — Profits from government-sponsored mortgage giants Fannie Mae and Freddie Mac, instead of taxpayers, would back up a home loan rescue for up to 500,000 strapped borrowers under a plan approved by a key Senate committee yesterday to pull the nation out of a housing crisis.

Democrats and Republicans banded together to push the plan through the Senate Banking Committee on a 19-2 vote, boosting the chances for a broad election-year housing aid package.

The centerpiece of the measure would give cheaper, government-backed mortgages to up to 500,000 strapped borrowers. Eight Republicans joined the panel’s Democrats to back it, after extracting a major concession to pay for the foreclosure-prevention plan by diverting money intended to pay for housing for the poor.

The bill also tightens regulation of Fannie Mae and Freddie Mac, which would finance a new affordable housing fund that would temporarily be used to pay for the foreclosure prevention program.

“If I were writing this on my own, it would look different, but it is a balance,” the Banking chairman, Senator Dodd, said. He also predicted the measure could clear Congress by July 4. “This is a major step forward.”

“I believe the White House will support this,” the panel’s senior Republican, Senator Shelby, said. “I don’t know why they wouldn’t.”

The White House, however, called that assessment premature.