The Government has said it will continue to consider contributions made by people to boost their state pensions after the April deadline passes.
At the moment, you can plug in any gaps on your National Insurance record as far back as 2006.
To receive the full new State Pension you need to have at least 35 years of National Insurance contributions, and ten years to get anything at all.
But after April 5, you can only purchase any missing National Insurance contributions going back six years.
Due to how busy the phone lines have gotten, the Department of Work and Pensions said if customers were unable to pay voluntary contributions for reasons beyond their control, it will consider payments made after the cut-off.
However, the considerations will be made on a case-by-case basis, depending on a person's individual circumstances.
The Government said it will take an "understanding approach" to the cases but didn't give examples of what reasons would be acceptable.
With this in mind, it is still best to make any National Insurance contribution purchases before the deadline if you can.
Not everyone will benefit from buying National Insurance contributions, and some people can top up their record for free. Check before you make a purchase.
There are examples of ways you may be eligible for National Insurance credits for free on the Gov.uk website.
The news first came to light after a recorded message was placed on a phoneline for the Future Pension Centre.
The message informed the public that there had been "unprecedented demand" on the DWP and HM Revenue and Customs (HMRC) phone lines.
The message told people they are expected to make every effort to make payments on time but "don't worry if you cannot get through".
A Government spokesperson confirmed the move in a statement reiterating what was said in the recorded message.
The spokesperson said: "Voluntary national insurance contributions do not always increase your state pension.
"Customers should make sure they would benefit before making any payments, including to fill gaps in their national insurance records between April 6 2006 and April 5 2016.
"The quickest and easiest way for customers to see information about their state pension and national insurance record is online. If customers need to contact us, we will ensure calls are answered as quickly as possible.
"If customers are unable to pay voluntary contributions by April 5 2023 for reasons beyond their control, we will consider payments made after the deadline on a case-by-case basis."
One reason the service has been slammed with calls is most likely due to the public awareness campaign fronted by the Money Saving Expert Martin Lewis.
Over the last year, the consumer rights champion has urged those aged between 45 and 70 to check their national insurance records to see if they could boost their state pension.
To receive the full new State Pension you need to have at least 35 years of contributions on your record.
On the pension special of his weekly ITV show, the Martin Lewis Money Show, Martin Lewis warned viewers that there were only six weeks left to make the contributions.
He explained that a voluntary £800 national insurance payment can add around £275 to your state pension and depending on how long you live after receiving the state pension, you could have a few thousand pounds added to your retirement fund.
