Efforts to shake up the housing market are gaining steam. Whether they’re enough to buoy all those houses under water remains to be seen.

The Obama administration’s heavily anticipated proposal to allow more deeply indebted homeowners to refinance is expected to be introduced this week, but it likely will fall short of a mass refinancing program favored by some economists and lawmakers.

Last week, Senate Republicans and Democrats came together to reinstate higher maximum loan limits for government-sponsored enterprises, such as Fannie Mae and Freddie Mac, and the Federal Housing Administration. The best-case scenario for both developments are minor improvements to homeowners’ housing burdens—and that prospect is an indication of the difficulty that policymakers will face as they try to end one of the worst drags on the economy.

The most immediate expected action is the Federal Housing Finance Agency’s rollout of a plan to enhance an existing program known as the Home Affordable Refinance Program by easing its eligibility requirements. The program is available to borrowers who are current on their loans but owe more than their home is worth and have mortgages backed by Fannie Mae or Freddie Mac that were originated before May 31, 2009.

HARP was originally meant to help as many as 4 million borrowers, who have been hit by home-price deterioration and lost equity, take advantage of low interest rates. The program, however, has reached fewer than 1 million borrowers, and tweaks to the program’s eligibility rules could qualify perhaps 600,000 more.

Analysts and mortgage-industry representatives tracking the changes said on Friday that it was unclear how quickly FHFA, which oversees Fannie and Freddie, would be able to operationalize them. They added that the agency’s handling of the changes and its coordination with lenders would be critical to success.

“It’s not going to be a mass refi program,” said Pete Mills, a managing director with the Community Mortgage Banking Project. Housing policy followers were also focused on the Senate’s passage late Thursday of an amendment from Sens. Robert Menendez, D-N.J., and Johnny Isakson, R-Ga., to reinstate the maximum loan limits for Fannie, Freddie, and the FHA to 125 percent of median house price with a cap of $729,750 in high-cost areas.

Rep. Scott Garrett, R-N.J., who plans to unveil a bill this week that would create a functioning private mortgage market without the GSEs, told National Journal he believed the Senate’s vote failed to recognize that Fannie and Freddie are costing taxpayers billions of dollars to cover their risk.

“The hypocrisy of Senate Democrats is at an all-time high. How can they claim the so-called ‘rich’ should be paying higher taxes and then turn around and say the American taxpayers should be on the hook for their mortgages?” he said.

Although House leaders rejected efforts to extend the limits this summer before they expired on Oct. 1, the 60-38 bipartisan vote gives the measure at least a 50-50 shot in the House, analysts said.

The National Association of Realtors and the National Association of Home Builders organized an intensive grassroots lobbying campaign to lift the loan limits. In separate interviews on Friday, Ron Phipps, the president of the Realtors’ association, and Jerry Howard, the head of the Home Builders, said they planned to apply heavy pressure to House members to convince them that altering government support for the mortgage market now would have deleterious results.

Senate aides who were on the floor during the vote said that the message seemed to be working. Sen. Herb Kohl, D-Wis., who had been a holdout as the only “no” vote among Democrats, was persuaded to change to “yes” and give the measure the 60 votes needed for passage, after a lengthy powwow on the Senate floor with Menendez and Senate Majority Leader Harry Reid, sources said. (Kohl has one of the most significant private mortgage insurance companies in his state, MGIC. Private mortgage insurance companies have opposed the loan-limit increase.)

“Senator Kohl became convinced that failure to pass the Menendez amendment would be detrimental, in the short term, to housing markets and the economy,” said Dawn Schueller, a spokeswoman for the senator.