(CNN) -- When homeless mothers in Sacramento, California, need food, counseling or support, they can come to a rectangle-shaped cinderblock building just a few blocks from the American River.
The building is home to Maryhouse, a daytime homeless shelter. Connie Frank is the executive director and it's her job is to connect the women with social services. Many of them need help finding nighttime shelter, counseling and food.
For Frank, the Women Infants and Children program is a key service.
"It's a wonderful program, an essential program, to feed these families," she said. "Baby formula, for example, is very expensive, and while we encourage women to breast feed, often they can't. Breast feeding moms need extra calories, and many of the women we serve can't get those extra calories while they are homeless, even if they are on food stamps."
Last year, 1,250 children came to Maryhouse -- a 29% increase. "It would make me sad to see fewer women eligible for WIC," Frank said. "It just adds to the long list of services that have been cut the past two years."
This spike in demand at Maryhouse and other social service programs across the country comes as House Republicans want to cut WIC by 10% as part of the 2011 federal budget plan passed last week, despite objections from Democrats and WIC advocates.
In addition to WIC, the GOP-controlled House also passed cuts to Planned Parenthood, arts programs and heating subsidies for low-income households.
Senate Democrats are proposing their own cuts they say total about $41 billion, although those cuts are based on President Obama's 2011 budget, which hasn't been passed.
They floated a plan on Thursday that goes beyond the $41 billion in cuts, but Republicans quickly responded that the proposal still doesn't cut deeply enough.
Obama has threatened to veto any bill that undermines the ability of the United States "to out-educate, out-build, and out-innovate the rest of the world." Obama has made WIC a spending priority, and is asking Congress to increase funding for the nutritional program for 2012.
A spending plan must be approved by March 4 to avoid a government shutdown.
Even if the Democratic Senate and Obama agree to WIC cuts, WIC has been running a surplus in 2011, and that money could be used to fill any funding reduction.
"The funding level that was provided last year...turned out to be more than what's needed," explained Zoë Neuberger with the Center on Budget and Policy Priorities.
"Participation didn't increase as much as was expected," Neuberger said. "Food prices ended up being lower than what was anticipated. And both because of the participation and lower than expected food costs, there are funds left over from 2010 that are available to be used."
One of the key reductions in food costs is the price of milk, which has declined by about a percentage point the past year. Milk makes up about 20% of WIC program expenditures.
If WIC is cut, it would be the first time the program has ever been reduced solely because of ideological reasons, according to Neuberger.
"It's definitely been a very popular program...And there has been a very strong bipartisan commitment in the past to make sure nobody gets turned away," Neuberger said.
"The question going forward is whether that commitment will be adhered to."