WASHINGTON (AP) — The Senate's two top leaders put on a show of comradery Monday as their chamber launched its immigration debate, but also laid down markers underscoring how hard it will be to reach a deal that can move through Congress.

"We really do get along, despite what you read in the press," said Senate Minority Leader Chuck Schumer, D-N.Y., at a previously scheduled appearance alongside his counterpart, Senate Majority Leader Mitch McConnell, R-Ky., at the University of Louisville.

There was even ribbing when Schumer presented McConnell with a bottle of bourbon made in his home New Yo...