As the longest government shutdown in U.S. history stretches into its fourth week, thousands of Coast Guard members and their families are preparing to go without a Jan. 15 paycheck. The Coast Guard is the only branch of the military affected by the shutdown, since it falls under the unfunded Department of Homeland Security, not the Department of Defense, which is funded for the year.

About 42,000 Coast Guard members are working without pay through the shutdown, having been deemed "essential" employees. An additional 10,000 civilian workers have been furloughed. The service managed to find enough money to make payroll on Dec. 31, but the continued lapse in funding means workers won't receive paychecks Tuesday. Last week, the Coast Guard said a prolonged shutdown could eventually hinder "mission readiness."

With no end to the political stalemate in sight, cash-strapped families of active service members are turning to organizations like the East Bay Coast Guard Spouses' Club in California for help staying afloat. On Sunday, the group said it helped 186 families at a food drive in a daycare center in Alameda, handing out supplies from the Alameda Food Bank.

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"It allowed them not to worry about a grocery bill this week," said Nicole Lauer, vice president of club.

Coast Guard members and their families attend a food drive in Alameda, Calif., on Jan. 14, 2019. CBS San Francisco

Lauer said the club had hosted events in the past to help families in the aftermath of natural disasters like wildfires, but never in response to a government shutdown. Lauer said items for babies and kids were quickly claimed. The club is planning another drive outside Base Alameda on Wednesday.

The Alameda County Community Food Bank has been providing food to local groups for distribution to Coast Guard families at events like the one on Sunday. Michael Altfest, the director of community engagement and marketing, said the food bank usually sees a drop in donations from businesses and individuals after the holidays, so the increased demand for assistance during the shutdown is coming at an especially difficult time.

And in California's pricey Bay Area, many people are already just one paycheck away from needing help.

"What happens is people often turn to us long after they should have," Altfest said.

Food and supplies are handed out to Coast Guard families at a food drive on Sun., Jan. 14, 2019. CBS San Francisco

Last week, CBS News' Janet Shamlian spoke to three Coast Guard wives in Bacliff, Texas, all of whom said they had to dip into their savings while they go without a paycheck.

"Our budget is extremely tight. We have just bought only the necessities when we went grocery shopping and, you know, trying to look at the sales and see what's on sale," said Vienna Julien.

Julien said Monday she was able to get essentials like diapers and baby food from a food pantry set up for Coast Guard families over the weekend, but the uncertainty over when the shutdown will end is still causing undue stress. Despite receiving some support, Julien said she has also experienced a lot of backlash from people who say Coast Guard families should stop being "greedy."

Lawmakers in the House and Senate have introduced legislation to pay Coast Guard members during the shutdown, but the bills have little chance of succeeding. The White House has said President Trump will veto any individual spending measures until Congress agrees to provide billions of dollars for border security.

Ashley Totten from Texas, whose husband serves in the Coast Guard, said families like her are "absolutely being overlooked" while other branches of the military continue to receive their pay.

"I think a lot of people forget. They definitely don't know what the Coast Guard does day to day," Totten said. "It's very frustrating as a wife to not see your husband get the recognition that he needs."

In a Facebook post Sunday, Adm. Karl Schultz, the Coast Guard commandant, tried to reassure families who might be struggling.

"While our Coast Guard workforce is deployed, there are loved ones at home reviewing family finances, researching how to get support, and weighing childcare options — they are holding down the fort," he wrote. "Please know that we are doing everything we can to support and advocate for you while your loved one stands the watch. You have not, and will not, be forgotten."