A McConnell spokesman did not immediately respond to a request for comment.
Isakson’s remarks came moments after he emerged from a closed-door meeting with Perdue and the top members of the Senate Appropriations Committee, their second in 24 hours.
One of those lawmakers was Patrick Leahy of Vermont, the panel’s top Democrat.
Read more: Capitol Hill push for Hurricane Michael relief could take weeks
“We’re very close,” he said. “I think we’ve got a bipartisan solution here.”
Some Democrats have been pushing for the Senate advance a $14.2 billion version of the disaster recovery bill that the Democrat-controlled House passed along party lines in January. The House bill includes several pots of money that were omitted from the Perdue-Isakson bill, including $500 million for climate resiliency projects in communities impacted by recent hurricanes and $68 million in Medicaid assistance to the Northern Mariana Islands, Guam and American Samoa.
The House bill would also expand full federal cost-sharing eligibility for certain storm damage in Puerto Rico and the U.S. Virgin Islands, a more open-ended change that has drawn Republican scorn.
Isakson wouldn’t share details about specific sticking points because he feared he could harm delicate negotiations. But he also expressed confidence that an agreement could be struck before March 15, when the Senate adjourns for a week-long recess.
“I will not try and beat somebody up over milk that’s been spilled,” he said. “I’ve just got to make sure we don’t spill any more.”
The movement on Capitol Hill came as Gov. Brian Kemp and Agriculture Commissioner Gary Black were set to travel to Tifton on Tuesday evening to talk with farmers struggling to recovery from Hurricane Michael’s damage.
Kemp and other local officials have upped the pressure on Georgia’s congressional delegation to advance the legislation in recent weeks.
“Let me be clear: Georgia families cannot wait any longer,” Kemp tweeted Monday. “I urge Congress to approve the proposal filed by @SenatorIsakson and @sendavidperdue as soon as possible. Livelihoods hang in the balance.”
Bloomberg reported Tuesday that lawmakers may also try to include aid money for the victims of the tornado that flattened portions of western Georgia and eastern Alabama over the weekend. Damage assessments are still being finalized.