According to this article, Brownback confessed to hating Clinton at one of the 'Family' meetings he was to speak at when he spotted her there, and asked for her forgiveness...also, notice the reference to the Clinton/McCain drinking contest below:
How Hillary Clinton turned herself into the consummate Washington player
by Joshua Green
Take Two: Hillary's Choice
Of the many realms of power on Capitol Hill, the least understood may be the lawmakers’ prayer group. The tradition of private worship in small, informal gatherings is one that stretches back for generations, as does a genuine tendency within them to transcend partisanship, though as with so much that is religiously oriented in Washington, the chief adherents are the more conservative Republicans.
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One spring Wednesday, a few months into the term, Senator Sam Brownback’s turn came to lead the group, and he rose intending to talk about a recent cancer scare. But as he stood before his colleagues Brownback spotted Clinton, and was overcome with the impulse to change the subject of his testimony. “I came here today prepared to share about this experience in my life that has caused great suffering, the result of which has deepened my faith,” Brownback said, according to someone who watched the scene unfold. “But I’m overcome now with only one thought.” He confessed to having hated Clinton and having said derogatory things about her. Through God, he now recognized his sin. Then he turned to her and asked, “Mrs. Clinton, will you forgive me?” Clinton replied that she would, and that she appreciated the apology.
“It was an extraordinary moment,” the member told me.
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Despite this chaos, Clinton managed to insinuate herself into the inner culture of the Senate almost immediately. Her operating belief seems to have been that the more her colleagues saw and knew of her, the more they would like her. This has indeed been the case. Almost every senator—especially every Republican—has a story of an early encounter with Clinton that, like Byrd’s and Brownback’s, invariably emphasizes the disparity between what they thought she would be like and what they saw when they actually met her.
Often Clinton’s dogged outgoingness—itself a subversion of her caricature—worked to reverse these old impressions, or pushed incidental encounters into prosperous partnerships. One of Clinton’s most enthusiastic and least likely fans is Senator Lindsey Graham, the South Carolina Republican who, when he was still a congressman, served as one of the most energetic managers of her husband’s impeachment.
Some of these odd-couple partnerships have their roots in symbiotic benefit: Rick Santorum, Newt Gingrich, and Bill Frist all made common cause with Clinton as a means of moderating their partisan image, just as she has used alliances with previous conservative critics to moderate hers. But Clinton has also displayed a subtler touch in the Senate than anyone could reasonably have expected, making especially good use of the ever-dwindling opportunities for casual commingling of members of the opposing parties. The Wednesday-morning prayer group is one. Another is the congressional delegation (“CODEL,” in Hill jargon), on which members travel together and wind up spending lots of time in close proximity. The story of one such trip, to Estonia, recently brought to light by The New York Times, gives a flavor of what Clinton is like in these settings. At a casual dinner with Senate colleagues Graham, John McCain, and Susan Collins, all Republicans, the waiter followed local custom by bringing a bottle of vodka and shot glasses, whereupon Clinton reached over and began pouring; a drinking contest ensued. McCain’s staff seemed pained by the revelation, and declined my request for an interview, because the last thing a Republican presidential hopeful wants floating around in the media is word that he’s becoming booze pals with Hillary Clinton. And McCain denied the story to Jay Leno. But when I recently intercepted him walking through the Capitol, McCain lit up at the recollection. “It’s been fifty years since I’d been in a drinking game,” said McCain, who as a former naval aviator knows whereof he speaks. He added, admiringly, “She can really hold her liquor.”
This repentance fostered an unlikely relationship that has yielded political bounty. Clinton and Brownback went on to cosponsor one measure protecting refugees fleeing sexual abuse, and another to study the effects on children of violent video games and television shows. “That morning helped make our working relationship,” Brownback told me recently. “It brought me close to someone I did not ever imagine I would become close to.” Since then, Clinton has teamed up on legislation with many members of the prayer group.
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http://www.theatlantic.com/doc/200611/green-hillary