Weir Farm has closed, but the post office is delivering, federal benefits checks are going out. However, Wilton will feel little direct effect, since the town gets little federal funding, if any.

Most federal benefits — Social Security checks, Medicare and Medicaid payments  — should go out as usual. And most veterans benefits are expected to continue — at least for a while.

But the federal shutdown will have a cost. Steven Lanza, editor of UConn’s quarterly state economic report, has warned that if the government were to shut for three or four weeks, it could cost 2,000 Connecticut jobs.

Weir Farm National Historic Site did close Tuesday, like other national parks.

“We’re in the process of pretty much buttoning down the park so the public is aware that the grounds and the buildings are closed,” said Linda Cook, superintendent of the park off Nod Hill Road.

“As a federal facility, it’s closed, and that includes the grounds as well,” Ms. Cook said. “We’ll have signs up where people would typically park, or enter the park.”

Weir Farm’s staff of eight full-time and six seasonal workers was busy Tuesday morning, closing things up, putting up signs. “We were directed to come in for four hours,” Ms. Cook said.

“There’s one employee who’ll be here in a caretaking status,” she said. “The other positions are directed to not access their email from home, to not do government work. They are on furlough. They’re temporarily relieved of their duties.”

Ms. Cook said Weir Farm does have a role as “an economic engine” — even if a modest one.

“On an annual basis our payroll is about $800,000 a year. It would fluctuate. We have a higher payroll in the summer than we do in the winter,” Ms. Cook said.

“There’s payroll. Then there’s also a number of contractors that work here, that then support local businesses,” she said.

“The visitors, the contractors, all the businesses we frequent, where our visitors shop, where our contractors shop to buy equipment or lunch or gas — the ripple effect is pretty substantive.”

Mr. Lanza, the UConn economist, spoke about the government shutdown at a press conference with U.S. Sen. Richard Blumenthal on Monday at Glastonbury-based manufacturer Habco.

Mr. Lanza said Moody’s Analytics has forecast that a shutdown of just a couple of days would show as negative consequences on gross domestic product growth.

“The consequences for Connecticut for just that 0.2 percentage point reduction in GDP would be a loss of 300 jobs and the associated incomes in Connecticut,” he said. “By loss I mean that the economy either would lose or simply not add 300 jobs it might otherwise have added. … That translates into $13 million in lost income on an annual basis to households here in Connecticut.”

The Social Security official website sought to assure the public that, while services would be reduced, the government would not stop sending out Social Security checks.

“Due to the federal government shutdown, Social Security field offices are open with limited services,” the website said.

“Social Security and Supplemental Security Income payments to beneficiaries will continue with no change in payment dates.”

The website lists some of the limited services that will continue to be provided at Social Security field offices, including help applying for benefits, assistance in requesting an appeal, processing a change of address, or direct deposit information.

Services the field offices won’t be able to provide during the shutdown include issuing new or replacement Social Security cards, replacing Medicare cards, and issuing proof of income letters.

The Connecticut Department of Veterans Affairs issued a statement Tuesday morning that veterans’ benefit payments would continue despite the federal shutdown — for a time, anyway.

But if the shutdown continues long enough, the payments could be affected.

“Due to the fact that some media are reporting that compensation, pension and disability checks will be interrupted by the government shutdown we are issuing this advisory to assure that all veterans and the media are aware that the interruption of these payments is not going to happen immediately,” said a release from Tammy Marzik, executive assistant to the Commissioner of the Connecticut Department of Veterans Affairs.

“We have learned that should the shutdown continue through the end of October, there is concern that there may be an interruption of these benefits,” it said.

Medical services provided by the federal Veterans Administration are expected to continue as well.

“It is important that Connecticut’s 52,000 veterans who use VA health care know that all VA medical facilities and clinics will remain fully operational, including pharmacy, inpatient/outpatient services,” the release said. “Additionally the compensation and pension claims processing and payments will continue to operate.”

Congressman Jim Himes, a Democrat whose 4th District includes Wilton, targeted “the House majority” — Republicans — in a statement Tuesday:

“As we emerge from another late-night session and move into the beginning of an avoidable and irresponsible government shutdown, I remain amazed by my colleagues’ unwillingness to put their own political agendas aside and do their job,” he said. “But because of the House Majority’s wish list of demands — including defunding or delaying health care reform just as it is going into effect — passport offices will shutter, businesses will see their federal contracts and loans delayed, and hundreds of federal employees living in Connecticut will be furloughed. Estimates show the American economy will suffer substantially if the government shuts down.”

“It is absolutely ridiculous that Congress would continue down this path of intransigence as the American people demand we find compromise and keep the government running,” he said.

US. Sen. Richard Blumenthal, another Democrat, said, “If calm minds and common sense prevail in bringing us together, there’s no question that a resolution can be passed by both houses of Congress that would continue government work in the service of the American people without the extortionist demands made by a small fringe group of extremists in the House of Representatives.”

And Democratic Sen. Chris Murphy emphasized that the shutdown would put most of the state’s 9,000 federal employees out of work.

“This is not about politics, as it seems to be for all these Tea Party Republicans,” Mr. Murphy said. “This is for the health of our economy.”