NEW YORK ( TheStreet) -- In a drastic effort to assist troubled homeowners, a California lawmaker plans to introduce legislation on Tuesday that would let just about anyone to refinance a mortgage into historically low interest rates. Rep. Dennis Cardoza (D., Calif.) wants to allow all homeowners with traditional, 30-year fixed mortgages backed by Fannie Mae ( FNMA.OB) and Freddie Mac ( FMCC.OB) to refinance into market rates, according to spokesman Mike Jensen. Unlike other government initiatives to help troubled borrowers, Cardoza's idea would ignore income, credit history or loan-to-value ratios to lower the cost of owning a home for up to 30 million homeowners. According to Freddie Mac, those mortgage rates are now running 4.37%, on average, down more than half a percentage point from April and far below rates in the years leading up to the mortgage crisis. Yet a recent study by the mortgage-information site Zillow found that nearly one-third of Americans can't qualify for a mortgage at all because their credit scores are too low, while more than half must pay above-market rates. A sweeping plan by the Obama administration called "Making Home Affordable" sought to help mortgage borrowers by plunging hundreds of billions of dollars into the mortgage-backed securities market to lower rates, and incentivizing banks to work out loans for distressed borrowers. Yet the plan has come under attack for its limitations that excluded millions of borrowers, and for failing to move many from "trial" modifications into "permanent" ones. Meanwhile, borrowers have complained - loudly and often - that they aren't getting enough help from big banks like Bank of America ( BAC), JPMorgan Chase ( JPM), Wells Fargo ( WFC) and Citigroup ( C), which service the vast majority of U.S. mortgages. From the point of view of banks and investors, it's not worth making a mortgage cheaper if a borrower can afford payments, and it's not worth modifying a loan if the borrower is likely to default anyhow. The situation has become a sticky Catch-22 for Democratic lawmakers and the Obama administration. Democrats face a tough election battle in November and want to connect with Main Street voters. The public feels as though banks received hundreds of billions of dollars' worth of taxpayer funds, while ordinary consumers are still struggling with massive financial woes. Cardoza is one of many House Democrats facing a challenge this fall. His proposal is part of a sharp change from his roots as a member of the "Blue Dog" coalition, a group of Democrats who insist on keeping the fiscal house in order. Although Cardoza voted for the $700 billion TARP bailout, stimulus funds and the Dodd-Frank financial-reform measure, he's also been railing against bank bailouts. He's also been issuing statements and funding for small-businesses and foreclosure relief.