"Rand Paul and I agree on most things. We don't agree on this," McConnell said. "We're just in a different place on this. Reasonable people can differ."
"Everybody threatens to filibuster. We'll see what happens," he said. "But we're talking about the security of the country here. This is no small matter."
The leader said he opposed a plan backed by the House of Representatives, that he said would effectively "end the program."
"I don't want us to go dark, in effect, and I'm afraid that the House-passed bill will basically be the end of the program and we will not able to have yet another tool that we need to combat this terrorist threat from overseas," he said.
The Senate will not vote on the NSA legislation until after it completes work on a bill providing President Obama with the "fast-track" authority to strike deals on trade.
In a rare political moment this week, Senate Republicans found themselves aligned with the president on the trade issue, while Democrats handed him a resounding defeat by voting against moving forward with the measure. Later in the week, Senate Republicans and Democrats struck a deal to advance the trade bill, setting up votes on amendments for early this week.
"We'll pass it later this week. The president's done an excellent job on this," McConnell said. "This is a trade promotion that is already not just for President Obama but for the next president as well. This is a six-year trade promotion authority bill that will give the next president an opportunity to enter into additional trade agreements with other countries around the world.
"The Senate's getting back to work," he said. "We're trying to focus on the things we can agree on that can make progress for the country ... even though we know there are many things we can't agree with the president on."
And as for the long awaited Bourbon Summit between McConnell and Obama?
"I'd be happy to do that, but we don't have a personality problem, we've just had differences on issues," McConnell said.