He also said they are negotiating a bill to combat the Zika virus and is "hopeful and optimistic" a deal can be reached soon and that floor debate could begin next week.
But conservative members in the House were blunt -- they said don't like a possible Senate short-term spending compromise and might try to block it.
"I think Leader McConnell is going in the wrong direction," said Texas GOP Rep. Bill Flores who told reporters he didn't believe it would pass the House. "Conservatives in the House would have an issue with that."
McConnell's upbeat assessment was a sharp turnaround from his remarks Tuesday when negotiations appeared stalled on the few key items Congress has left to do before the November election. But the driving motivation for the GOP leader is to get the two contentious issues -- spending and Zika -- behind him and let his vulnerable members facing re-election go home to campaign.
"The single biggest piece of business we need to conduct is to get the government funded before the end of the fiscal year," McConnell told reporters after meeting privately with his caucus for the first time since senators returned from a seven-week recess.
McConnell would not say if government funding and Zika would be joined into a single bill although several senators in both parties believed they would end up in one package.
Senate Minority Leader Harry Reid also said he hopes "to do something quickly," but warned his party would block bills that included what Democrats consider poison pills, like restrictions on funding for Planned Parenthood and cuts to Obamacare in the Zika bill.
Speaking to the potential showdown with conservatives in the House, Reid described those provisions as unacceptable "Freedom Caucus bells and whistles."
The Democratic leader said the tangible progress on the two issues was positive enough that he dropped his threat Tuesday to shutter action in Senate committees to force action on Merrick Garland's stalled Supreme Court nomination.
But the concerns of the House Freedom Caucus, the group of members on the right, are real and without their votes it's likely House Speaker Paul Ryan will have to turn to Democrats to pass a funding bill.
This bloc of conservatives, along with several outside advocacy groups on the right are arguing that Congress should pass a funding bill that lasts through the spring. They want to avoid a lame duck session because they worry any broader spending deal negotiated in December will be a deal with items they oppose.
Rep. Mark Meadows, R-North Carolina, said he and other conservatives in the Freedom Caucus prefer a spending bill that funds agencies through the spring. But Meadows acknowledged that he and some are open to something else if leaders agree to add a provision that would impose a "temporary pause" on refugees from Syria and other Mideast countries with terror ties to come to the United States.
"If that were something that could be guaranteed in the short term (continuing resolution) I think you'd see a majority of Freedom Caucus members supporting a short term strategy," Meadows said, saying they believed it was "a reasonable request."
That idea will be a non-starter for Democrats. And again, when faced with a pre-election deadline, GOP leaders will come under pressure to avoid any policy provisions that will cause Democrats to bolt.
House Appropriations Committee Chairman Hal Rogers has said he supports a similar approach as McConnell's -- a bill through some time in December -- and said that there are some discussions about attaching Zika money to the must-pass bill, although no decisions have been made.
Asked if adding Zika could help attract Democratic support for a package, Rogers said: "I think so"
House Minority Leader Nancy Pelosi held a news conference with public health advocates and physicians pushing for Republicans to take up a "clean" bill funding Zika efforts.
Ryan, asked about moving a Zika bill without controversial policy riders on it, sidestepped the question and blasted Senate Democrats for blocking action on a Zika measure on Tuesday night.
"Give me a break on this one. We passed the $1.1 billion bill for Zika, which was the level agreed to in the Senate," he said.
But Ryan added: "This is obviously an issue we are going to have to resolve this month."
Previously, Pelosi had insisted that Congress give the Obama administration the full $1.9 billion it requested to fight the epidemic, but on Wednesday she just stressed that whatever Congress does it "has to be for a year."
A Pelosi aide said the $1.1 billion in the Senate measure meets that criteria.