NEW YORK ( TheStreet) -- The Obama administration is exploring plans to allow more borrowers to refinance at lower rates. Any measure would face stiff opposition in Congress. Senators Bob Menendez (D, N.J.) and Barbara Boxer (D, Calif.) reintroduced legislation Thursday aimed at removing barriers that prevent borrowers with government-backed loans from getting the lowest possible interest rates. The Responsible Homeowners Act of 2013 would improve upon the government's current Home Affordable Refinance Program (HARP) by eliminating appraisal costs, reducing upfront fees on refinances, ensuring consistent standards for all lenders and providing equal access to refinancing options to all borrowers, the senators said. The legislation was introduced last year but failed to win Congressional approval. "We need to bring much-needed relief now to hard-working, responsible homeowners who are struggling to keep up with their high interest-rate loans -- including thousands in New Jersey whom I have heard from," Menendez said in a release. "We need to do this before interest rates go up again. It's time that Congress finally put families first and give homeowners who have played by the rules a fair chance to refinance at today's low rates." The administration's current HARP program allows borrowers with loans backed by Fannie Mae and Freddie Mac to refinance at lower rates even if they owe more than what their mortgages are worth, so long as they are current on their payments. The program, which was expanded in October 2011, has helped 1.8 million borrowers and boosted the refinancing business for banks including Wells Fargo ( WFC), JPMorgan Chase ( JPM) and U.S. Bancorp ( USB). But borrowers have still not fully benefited from rock-bottom interest rates because the program currently is structured in a way that limits competition among lenders. Under HARP, a bank that wants to compete with the current lender for business has to go through tougher underwriting criteria and faces greater risk that Fannie Mae or Freddie Mac would force them to repurchase loans should the borrower default. As a result, the borrower finds he can often get his loan refinanced only with his current lender and is not able to shop around for a better rate. That allows lenders to charge higher rates.