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The biggest arguments of the day will be inside the Supreme Court, but just off the steps this morning two demonstrators from opposite camps debated the merits of health care overhaul for about 20 minutes, and even reached a sort of truce by the end.

The two sides were represented by Bruce LaPorte, a Tea Party libertarian from northern Virginia, and Paula Waterman, a retired federal worker from Maryland.

Waterman, who was sitting in a chair and holding a pro-Obama poster, steered the conversation by arguing that the health law would help fix abuses by doctors who she said care more about making money than helping patients. LaPorte, who wore a cowboy hat and held an anti-Obama sign, mostly listened and argued that "Obamacare" is a government takeover.

But LaPorte couldn't help but agree with Waterman briefly.  "I agree there's abuses by the doctors," LaPorte said as pro-Obama demonstrators chanted loudly just to his right. "But government taking it over is not the solution."

Waterman argued that the health care law isn't a takeover, and that insurance companies' CEOs shouldn't be making big bonuses. LaPorte agreed with that and said the difference between his Tea Party faction and the Occupy protesters is that he wants his money back, not a government bailout.

LaPorte said a "government solution" interferes too sharply with the private sector. Waterman said that "it is the solution for now."

The conversation turned to Wall Street, perhaps naturally, and they found plenty of shared sentiment there: the bankers are bad and both parties take too much money from them. They shared some laughs about disgraced investment adviser Bernie Madoff, and how his last name is indicative of his crime.

Then Waterman had an idea. Why not team up, these two diametric enemies, and take on Wall Street together? "If you and people like me get together …" she began.

"We have common ground on some of the things that need to be addressed," LaPorte acknowledged, smiling.

"It isn't hard to remain civil," Waterman laughed.

As they broke off their talk, LaPorte mentioned that he's a libertarian.

"Good going," Waterman said.