It is only a first step toward healing the economy’s biggest open wound, but President Obama’s new mortgage refinancing plan could provide considerable relief for millions of homeowners shackled to high interest rates. If Congress approves it — unlikely, with resistance already mounting from Republicans — the plan could also put money in pockets and cash registers at a time when that is desperately needed.

Interest rates are now at historically low levels, but banks refuse to let millions of homeowners refinance, because their credit is not stellar or because their homes are worth less than what they owe. High fees and intimidating red tape have kept many borrowers from even trying.

Last fall, the White House announced a plan to help as many as 11 million homeowners by relaxing refinancing rules for mortgages held by Fannie Mae or Freddie Mac, the government-sponsored companies. But neither has agreed to eliminate appraisal costs and other fees, or to ease the application process. The president’s new plan, announced last week, asks for legislation to require those changes.

There are millions of other borrowers with loans held by banks, which have largely not responded to pressure to relax their refinancing standards. The new plan would allow those homeowners to refinance into new low-interest loans backed by the Federal Housing Administration.

Currently there are limits on the F.H.A.’s ability to guarantee loans bigger than the value of a property, and some homeowners could walk away from their loans and leave taxpayers with the bill. To cover those potential losses — estimated to be $5 billion to $10 billion — the White House is asking for legislation to impose a fee on big banks.

In most cases, though, the reduced interest rate and monthly payment would most likely keep families in their homes (especially because only borrowers who were current on payments would be eligible), thus reducing defaults. Some might apply the extra money to the equity in their homes, bringing them up from being underwater, while others would stimulate the economy with new spending.

Though useful, Mr. Obama’s new proposal would have a stronger effect if he combined it with forceful efforts to get Fannie, Freddie and private banks to reduce the principal on underwater loans. The proposal would significantly increase financial incentives for lenders to write down the principal on these loans, an action that can be taken by the Treasury Department without Congressional approval.

But incentives go only so far. Fannie and Freddie need to push lenders to agree to more principal reduction, and need to be pushed themselves, with legislation.

The program demonstrates a clear contrast with Republicans, both in Congress and on the presidential campaign trail. Many, including Mitt Romney, want the government to do nothing to help homeowners on the verge of foreclosure. That should not stop the White House and other Democrats from vigorously making the case that there is an alternative to that coldhearted prescription, if lawmakers would just seize it.