Despite his reputation outside Washington as a liberal ideologue, Sen. Edward Kennedy (D-Mass.) is revered by his adversaries on Capitol Hill for being the chamber’s greatest dealmaker and Republicans sensed his absence as much as Democrats did Wednesday.

The 76-year-old political icon’s sudden diagnosis of a malignant brain tumor had many GOP senators lamenting a more complicated upper chamber without Kennedy, who has routinely reached across party lines on a wide number of issues to cut landmark deals.

Sen. Judd Gregg (R-N.H.) recalled months of closeted meetings in 2001 with Kennedy that culminated in the No Child Left Behind law. Senate Republican Conference Chairman Lamar Alexander (Tenn.) could go back as far as 1967 — Kennedy’s first term in the Senate — to chart his history of compromises.

“He’s a legislator’s legislator. At the end of the day, he wants to legislate, he understands how, and he understands compromise,” said Kyl, who recalled “very intense, very, very hard” negotiations over the immigration bill that ultimately failed last summer. “It confirmed what I knew about him. And it’s worth talking about because it shows how people with drastically different points of view can come together.”

On occasion, Kennedy’s readiness to compromise has irritated even his fellow Democrats. In 2003, for example, he initially backed the Senate Medicare prescription drug bill, putting him at odds with much of his conference and specifically then-Senate Minority Leader Tom Daschle (D-S.D.).

But GOP senators like Alexander say that sense of compromise is nothing new, and indeed hasn’t wavered since the ’60s. Alexander came to Congress in 1967 as an aide to then-Sen. Howard Baker of Tennessee and worked with Kennedy near the end of his first term.

“I’ve known and worked with him for 40 years. He’s results-oriented. He takes his positions, but he sits down and gets results,” Alexander said. “We’ll miss him greatly and hope he’s able to recover.”

Kennedy was diagnosed Tuesday with a malignant glioma, a cancerous tumor on the left frontal lobe of the brain in an area that controls speech and movement. Massachusetts General Hospital discharged Kennedy Wednesday so he can recover at his Cape Cod home.

His physicians said Kennedy “has recovered remarkably quickly” from his biopsy Monday and that future treatment plans have yet to be determined.

Quiet positioning for Kennedy’s coveted chairmanship of the Senate Health, Education, Labor and Pensions Committee could start soon, depending on how long he stays absent. Sens. Chris Dodd (D-Conn.) and Tom Harkin (D-Iowa) are next in line, but since both already have chairmanships, Sen. Barbara Mikulski (D-Md.) could get the nod.

In a larger sense, respected Democrats who could fill Kennedy’s role as a dealmaker include Dodd or Sen. Dianne Feinstein of California. Some GOP senators also suggested Majority Whip Dick Durbin (D-Ill.) as a more remote possibility.

In the meantime, his Republican rivals joined Democrats in wishing him a speedy recovery and recalled his passion for striking bargains that result in public policy.

“He can make a strong statement for the left but at the same time understands how to govern from the middle,” Gregg said. “Politics in America is played at the 40-yard lines. You can stand there and shout, but you’re not going to get anything done until you get to the 50.”

Sen. Lindsey Graham (R-S.C.) cut deals with Kennedy often based on a simple handshake or promise, such as legislation governing U.S. policy towards foreign detainees.

“When we worked on the detainee bill it was just members of the Senate and members of the executive branch literally writing a bill, line by line,” Graham said. “He told me it was like the Civil Rights Bill, where you just put people in a room and you wouldn’t let them out.”

Fellow Republican Sen. Mike Enzi of Wyoming, the ranking member on the Senate HELP Committee, said one unfortunate result of Kennedy’s success is the lack of attention it receives outside the Beltway. Because Kennedy is so skilled at untangling conflicts, in other words, national media often don’t pay attention to the results.

“But that’s much better than getting nothing done, which is what usually happens around this place,” Enzi said. “And you’ll notice those bills usually pass unanimously or near-unanimously.”