Sen. Joe Lieberman (I-Conn.) said the vote showed that both Republican and Democratic members of the Senate saw the need to do something to keep the mail service from going into the red.

"We may differ on how to react to the crisis but this strong cloture vote that three quarters of the members of the Senate at least are ready and eager to debate and can pass something that will save the postal service from bankruptcy," Lieberman said.

Just before the vote, Lieberman urged members of his chamber to vote to move forward on the motion, saying a vote against cloture was essentially a vote against keeping the service out of bankruptcy.

"If you vote against cloture, you're essentially saying you don't want to do anything," Lieberman said.

Lieberman stressed that the legislation would streamline the service while also avoiding "draconian" cuts.  

Speaking after Lieberman but ahead of the vote, Sen. Susan CollinsSusan Margaret CollinsOvernight Health Care: 3.6M signed up for ObamaCare in first month | Ryan pledges 'entitlement reform' next year | Dems push for more money to fight opioids Study: ObamaCare bills backed by Collins would lower premiums Right scrambles GOP budget strategy MORE (R-Maine) said failing to move the legislation forward would be delivering a "critical" blow to the mail service.

"If we fail to act, we will deliver a critical, crippling blow to the Postal Service. As Sen. Lieberman has indicated, the postal service is in crisis. It has lost more than 13 billion dollars in the past two years," Collins said. "We have to address this crisis."

Collins warned that 8.7 million jobs were at stake with the Postal Service and that it is the linchpin of a "trillion dollar mailing industry."

"It would be irresponsible for members to vote no on the motion to proceed if they have," Collins added. "We simply cannot allow the postal service to fail. The stakes are too high for our economy and for Americans across this country. Finally, I would remind our colleagues that the Postal Service goes back to the roots of our Constitution. This is an organization that is vital to our heritage and to our future. "