Even when opposition-party legislators express a genuine willingness to work cooperatively while they're in the Oval Office, that impulse often begins to fade when they hit the White House driveway, says Mike McCurry, who served as Clinton's spokesman.
After Gingrich met with Clinton, McCurry says, the president often would relate to his staff the progress that they had made. But then "when Gingrich was surrounded by Dick Armey and some of the other Republican leaders, he wasn't nearly as forthcoming as he had been in some of the private conversations," McCurry added.
"That's where it gets difficult," McCurry said. "They have to continue to fly the flag afterward, and that is one of the reasons why it's hard to make progress."
The fact that Obama's meeting with congressional Republicans is such high-profile news is a sign itself of how things have changed, and not for the better.
Meetings between presidents and congressional leaders of both parties used to be humdrum, says Calvin Mackenzie, a presidential historian at Colby College.
"Lyndon Johnson would sit down with (Senate Minority Leader) Everett Dirksen at the end of the day. They'd have a drink. They'd do business together and that was the norm," says Mackenzie. "Now those norms are out the window. We have a much more divided set of institutions."
In today's highly partisan environment, says Mackenzie, talk about working together for the common good "evaporates very quickly" once the meeting ends.
In one recent high-profile meeting, the good will didn't even last that long.
In September 2008, as U.S. financial markets were seizing, Republican presidential candidate John McCain made a dramatic call for a break in the campaign so that he and Democrat Barack Obama could meet with Bush and congressional leaders.
With the candidates, congressional leaders and administration officials all crowded into the Cabinet Room, Bush opened the meeting by stressing the urgent need for legislation to bail out the financial industry. Treasury Secretary Hank Paulson spoke about the volatile financial markets. Obama spoke next. Then, the president called on McCain. He passed.
From there, Bush wrote in his memoir, "what had started as a drama quickly descended into a farce. Tempers flared. Voices were raised. Some barbs were thrown. I was watching a verbal food fight, which would have been comical except that the stakes were so high."
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