The federal government is shut down, but that hasn’t stopped agencies from running lots of “help wanted” ads.

More than 4,000 job postings remained active on the federal government’s hiring site as of Tuesday. Although many ads first ran before the shutdown began, nearly 500 posts were placed in the past three days.

The vacancies include some high-priced positions: a media relations officer job paying up to $155,000 at the Centers for Medicare & Medicaid Services, the agency in charge of implementing Obamacare, and a senior communications and marketing specialist for the Patent and Trademark Office, making up to $136,000.

The newly created Consumer Financial Protection Bureau placed an ad Friday for a chief of staff to the chief information officer, a position that advertises a salary of $121,000 to $224,000.

With so much of the rest of the government closed, including national monuments and parks, the advertising of so many job postings raises larger questions about the shutdown, according to one government watchdog.

“It goes to the whole discussion about how much of a shutdown this really is in the first place,” said David Williams, president of the Taxpayers Protection Alliance.

“It’s more of a slowdown or a selective shutdown where they’re shutting down things that are getting the biggest bang for the PR buck,” Mr. Williams said. “It’s a strange thing to be shutting down memorials and, at the same time, they keep trying to hire people. That makes no sense.”

The government’s hiring database — usajobs.gov — is run by the Office of Personnel Management, which has notified the public that some of its websites might not work until after the shutdown. Still, the jobs site, which the agency says isn’t funded with annual appropriations, seemed largely unaffected.

On Tuesday alone, agencies posted at least 182 new job ads, including a supervisory information technology specialist at the Office of the Comptroller of the Currency offering a salary of $98,000 to $182,000 per year.

While many ads offered jobs at the Department of Veterans Affairs, which the House has voted to exempt from the shutdown, other agencies posting ads included the departments of defense, energy, homeland security, justice and Treasury.

Several agencies, such as the Commerce Department, weren’t available to discuss the hiring efforts and their newly placed job ads. Calls to public information offices were met with voicemail messages saying nobody could return calls until after the shutdown. Among other agencies, the Consumer Financial Protection Bureau isn’t funded by congressional appropriations, so it isn’t impacted directly by the shutdown.

Kathryn Troutman, founder and president of The Resume Place Inc., which specializes in helping government job seekers, said there is no doubt about a hiring slowdown.

On average, her company handles about 50 resumes every two weeks, but it’s now down to 15 resumes. Still, Ms. Troutman said, the federal government isn’t going anywhere. She is optimistic that activity will pick up soon.

Although federal workers have been shaken by job insecurity, they are still in better shape than many contract employees in the private sector, she said.

“The one thing you could count on is that the federal government is a stable employer, but that’s a little questionable right now,” Ms. Troutman said. “The feds have been very lucky, but I don’t think it’s so safe anymore.”

The Centers for Medicare & Medicaid Services media affairs job was posted the day after the shutdown began. The job description says the employee will be “providing proactive consultation to senior staff with respect to relations with all varieties of media and promoting the vital work performed by [the agency] in maintaining and improving the nation’s health care.”

Emma Sandoe, a spokeswoman at the Centers for Medicare & Medicaid Services, said much of the agency’s press office has been placed on furlough. She said the job posting for a media relations officer was set to appear on the jobs site before the shutdown.

Many of the job ads are set to expire in days, and applications are likely to pile up on the desks of out-of-work human resource officers.

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