AFGE also pointed out that the budget currently funding the federal government will expire in March, raising further questions about if eight months of pay could be guaranteed.
But it remains unclear how many people will take up the offer. According to CNN, the Trump administration is planning to implement widespread layoffs for employees who decline it, leaving further uncertainty for those who remain.
Federal employees who spoke to the BBC described an atmosphere of confusion and anxiety, as they weighed what comes next.
One woman who spoke on the condition of anonymity said she had been a federal employee for more than two decades.
“It appears rude and appalling,” she said, adding the offer itself seemed “threatening, e.g. ‘take it or leave it or your job might be eliminated anyway'”.
And there is “no guarantee” for the buy-out programme, she added.
Even workers who said they would take the offer expressed similar concerns: that they may not get the pay they have been promised.
Another federal worker said while he planned on taking the offer, he was not confident.
“I hope that it will be exactly what’s promised, and not a scam,” he said.
Trump’s efforts to cut down on the size of the federal government – with major input from tech billionaire Elon Musk – have been applauded by many leading Republicans, who control both chambers of Congress.
House Speaker Mike Johnson said during a press conference on Wednesday that the “stewardship of precious American taxpayer dollars” was being well-handled.
“That is a long overdue, much welcome development,” he said.
But Trump’s efforts to overhaul the federal government – coupled with a number of other major moves, including a crackdown on immigration and his decision to ban diversity, equity and inclusion efforts in government – has also inspired the first nationwide protests against the president this term.
Thousands protested against the reforms across the country on Wednesday.
Numbers were in the dozens at many of the protests, but in demonstrations like Michigan, more than 1,000 people turned out, local media reported.
BBC News