He added, "If I only dealt with my Republican colleagues only on an issue basis, I probably never would get anywhere. But I deal with them on a human basis, too."
Alexander, who first came to the Senate as an aide in 1967 for former Sen. Howard Baker and later served as a liaison between the White House and Congress, said Obama's relationships with Congress and with the opposing party in particular are a far cry from previous presidents.
Alexander, who recently announced he would step down from GOP leadership to better build bipartisanship, said that it has hurt Obama's agenda.
But Sen. Jay Rockefeller (D-W.Va.) dismissed the idea that more outreach from the White House — phone calls, visits and the like — would work, given today's political environment.
"It doesn't get any bills passed," he said. "It wouldn't be a very good use of his time."
Former Sen. Scott Brown, R-Mass., candidate for U.S. Senate in New Hampshire, holds his hand over his heart during the singing of the national anthem as he waits to take the stage for his town hall campaign rally with Sen. John McCain at the Pinkerton Academy in Derry, N.H., on Monday, Aug. 18, 2014.