Gov. Charlie Baker hopes to have a plan by next week to share with the Legislature to extend financial support to the thousands of federal workers living in Massachusetts who are going without pay during the government shutdown.

The federal shutdown entered its 34th day on Thursday with President Donald Trump and Congressional Democrats still deadlocked over Trump's demand for $5.7 billion to fund a wall along the southern border.

Massachusetts is home to about 47,000 federal employees, including about 7,000 impacted by the partial federal government shutdown, according to state and federal officials.

"The biggest things we're concerned about is their ability to pay their rent and their mortgage and sort of the cost of daily living since many of them are either working without getting paid or being sort of nudged into not looking for other work, and what we've been working most on is trying to figure out how to make the unemployment insurance system support these folks," Baker said Thursday.

"Our goal is to have some thought about how to do that that we can talk to the Legislature about next week," he said.

The House and Senate were also taking steps Thursday toward intervening to help federal workers.

The House gave initial approval to a resolve (H 73) from Rep. Natalie Blais and Sen. Jo Comerford to create a Massachusetts Government Assistance Task Force. That task force would be directed to report by Friday, Feb. 1 on action steps for the state to take and "an analysis of government programs impacted, how Massachusetts residents are affected, and the potential cost and economic impact to the commonwealth during a short term and long term shut down."

"As this extends for a longer and longer period of time, there are going to be a number of people there that obviously are not going to be in a good position in terms of paying bills and whatnot, because of the fact, obviously, they're getting no income. So what I'm hoping is that we can get an answer in terms of what we might be able to do, what we can do, what options are open to us here in Massachusetts to help these people out," House Speaker Robert DeLeo told reporters.

Baker, DeLeo and Senate President Karen Spilka first started talking about the possibility of extending unemployment benefits to federal workers over a week ago during their private, semi-regular Monday meeting. An aide to DeLeo said the idea of a task force has also been discussed with Baker.

The Senate adopted an order Thursday creating a seven-member group to develop recommendations to mitigate shutdown impacts on Massachusetts residents.

Baker said his administration has also created a "pretty robust portfolio" about the shutdown that "goes way beyond the folks who work or contract with the federal government," and would also likely share that with the House and Senate.

The Massachusetts Nonprofit Network said Thursday that organizations it represents are experiencing "delays in current grant programs, uncertainty around entitlement funding, and little to no federal technical assistance on grant and program administration."

Nonprofits are also seeing delays in upcoming grant cycles, lapses in federal approvals necessary to do their work and a "reduced ability" to carry out daily operations.

"The results of the survey speak to the incredible strain on nonprofits caused by the uncertainty of federal funding and increased demand for services," said Jim Klocke, CEO of the Massachusetts Nonprofit Network. "Many organizations are on the front lines serving furloughed federal employees and others who are impacted by the shutdown."

Erin McAleer, president of Boston-based nonprofit Project Bread, said that recipients of supplemental nutrition benefits, or food stamps, are also "confused and anxious," despite SNAP benefits being guaranteed through February.

"We are hearing from more people who need help accessing food, including furloughed federal employees. Mitigating the impact of the shutdown is our top priority, but as a nonprofit, the attention the shutdown demands is consuming significant resources and staff time across our entire organization," McAleer said.

Katie Lannan and Sam Doran contributed reporting.