Donahoe wants lawmakers to eliminate the retiree prefunding requirement and allow the Postal Service to control its own health-care system. The mail carrier expects to default on its next $5.6 billion payment to the Treasury for the future retirees' health-care fund due in September.
(Read more: US Postal Service loses $1.9 billion in second quarter)
The semi-independent government agency relies on the sale of stamps and other products rather than taxpayer dollars to fund its operations. Revenue from first-class mail, its most profitable service, decreased by $198 million in the second quarter of fiscal year 2013.
"We cannot pretend these marketplace changes aren't happening or that they don't require us to make fundamental changes to our business model." Donahoe said. "We need legislation that, together with our planned changes, confidently enables at least $20 billion in savings by 2016. If not, we go over the edge."
The Postal Service's pleas for flexibility have so far gained little traction as Congress has several times failed to pass legislation allowing it to modify its operations.
"Ultimately, we've kicked the can down the road, first in 2006 by not doing enough and every year since," said Rep. Darrell Issa, R-Calif., oversight committee chairman and a supporter of a five-day mail delivery schedule.
"We in the House, we in the Senate must get together and we must do it this year," Issa said about a Postal Service overhaul.
But the Postal Service still faces a Congress that remains gridlocked on reform and preoccupied with other legislative priorities.
(Read more: Desperate US Postal Service tries to find its 'cool' factor)
On Wednesday, Rep. Elijah Cummings, the top Democrat on the oversight committee, questioned Issa's push for five-day delivery.
Cummings has introduced a bill that would create a new position for a chief innovation officer to develop more competitive products for the Postal Service.
It would also permit the Postal Service to provide non-postal services, such as check-cashing, warehousing and logistics and public Internet access as alternative ways to raise revenues. Cummings' bill would also delay the next payment into the health-care prefund until 2017.
"If we reject extreme measures that harm postal workers, increase the Postal Service's debt and destroy existing services, I believe we can identify common-sense provisions that provide common-ground solutions," Cummings said.