In response, he said he will bring up a "freestanding" bill next week to commit roughly $5 billion to address the humanitarian part of the crisis.
McConnell, R-Ky., said the money was supposed to be included in a recent bill to provide emergency funds to areas hit by storms, but the Democrats insisted the funds be removed.
"I'm going to bring it up freestanding next week and see if they really aren't interested in dealing with this mass of humanity that we have to take care of at the border. What's the objection? he asked.
He stressed that the bill would focus on the humanitarian issues, not President Trump's border wall, which is vigorously opposed by Democrats.
"I think it's safe to say the president is getting more cooperation out of Mexico than he is out of congressional Democrats," said McConnell.
He said Democrats are "suffering from Trump Derangement Syndrome" and whatever he supports, they will "reflexively" oppose.
"We want to build a wall. We think the president has made a good case for that. That's not what this is about. This is just the humanitarian part of the problem on our side of the border," he said.
McConnell responded to the clip by stressing that the Senate has "never failed" to address the issue, adding "I'm not sure why he's all bent out of shape."