Under the swap program, domestic bondholders, mostly pensioners, have to exchange government bonds for lower value ones and with zero coupon until 2024 before they will earn interest.
President Nana Akufo-Addo, who reversed course about going to the IMF last year, has called on Ghanaians to back his government's effort to end the economic crisis.
But some bondholders have opposed the deal ahead of the January deadline.
"That's totally unfair and the government cannot pass on the mess it created to us to bear," Benjamin Aidoo, a 65-year-old retired doctor, told AFP.
"We have school fees to pay. We have medical bills to clear. Some of us are owing rent and we have invested our retirement packages into government financial instruments to settle those debts. How does the government expect us to survive if we agree to this program?"
Ghana reached a staff-level-agreement with the International Monetary Fund (IMF) in December as part of its efforts to pull out of its worst economic crisis in decades.
The debt restructuring is needed before the IMF board will approve the relief package and Ghana has defaulted on most of its external debt and has requested to restructure its bilateral debt.
After meeting this week with the individual bondholders, Finance Minister Ken Ofori-Atta said securing at least 80 percent participation will put Ghana in a better position to secure the IMF deal.
"I think the clarity for all of us is that it is a voluntary program," Ofori-Atta told the media on Thursday.
"We've anticipated maybe getting up to 80 percent which will still put us within the parameter. So, we are asking everybody to really join."