Democrats on Thursday criticized Republican front-runner Mitt Romney’s suggestion this week that he might eliminate the Department of Housing and Urban Development, warning that such a step would put recent reductions in veterans’ homelessness at risk.

In a conference call with reporters sponsored by the progressive Truman National Security Project, speakers said that eliminating the department would put an end to a voucher program that has provided housing to more than 30,000 homeless veterans in recent years.

“Where would these people go if Mitt Romney had his way?” asked Rep. Bob Filner (D-Ca.), the ranking Democrat on the House Veterans Affairs Committee. “They would be back on the streets.”

The program, known as HUD-VASH, is a joint effort with the Department of Veteran Affairs that combines housing vouchers issued by HUD with supportive services from the VA for chronically homeless veterans.

Advocates for the homeless give the program much of the credit for a 12 percent reduction in the number of homeless veterans counted on the streets between January 2010 and January 2011.

“A big part of that is the HUD-VASH program,” said Tammy Duckworth, a former assistant secretary of public and intergovernmental affairs for the VA in the Obama administration who is running as the Democratic nominee for a congressional seat in Illinois.

During the conference call, Duckworth said that the program saves taxpayers’ money, citing data showing that medical care for homeless veterans is twice as expensive as it is for those in housing.

VA and HUD want enough funds to issue 10,000 more vouchers a year through 2014 as part of the Obama administration’s plan to end homelessness among veterans by 2015.

Democrats have seized on Romney’s remarks about HUD, which were overheard by reporters at a private fundraiser, as evidence that he is unconcerned about the poor.

“It boggles the mind that Governor Romney would feel this is an acceptable way to treat vets,” Duckworth said.