Senior House Republicans want to overhaul the financing of the housing market, offering a plan to get government mortgage giants out of the mix and let the private sector take over.According to Politico , the proposal unveiled Thursday by Financial Services Committee Chairman Jeb Hensarling of Texas would eliminate most taxpayer support for the housing market.The idea has grown out of the discontent among lawmakers over the 2008 bailout and government takeover of mortgage giants Fannie Mae and Freddie Mac.If passed, the GOP proposal likely would increase mortgage costs for borrowers, a situation Democrats likely would object to. But Hensarling doesn't believe that's necessarily a bad thing."We believe that more people would have an opportunity to buy homes that they can actually afford," he told reporters, according to Politico. "Today we have a system where the Washington elite decide who can and cannot qualify for a mortgage.""We have a set of policies that caused taxpayers to have to shell out $187 billion in bailouts for Fannie and Freddie," he said. "Today the federal government has what is known as a virtual monopoly of the housing-finance system. That has to change."Predictably, Democrats don't agree with the approach."He wants to get rid of Fannie and Freddie, and I think there's a way to do that, to unwind those, but I think his approach would make a 30-year mortgage rate at a fixed rate or so incredibly high that it would be beyond the reach of most consumers," Rep. Stephen Lynch, a Massachusetts Democrat, told Politico. "He may lose support on his own side."Republicans say they want to be sure the measure does not make it harder for lenders to finance mortgages, and that they would be opposed to any proposal that constricts the market.Speaker John Boehner and other GOP leaders have signaled their support for the Hensarling measure.