The background: When asked by a viewer at the CNN-YouTube debate if he would meet with the leaders of rogue nations without preconditions during his first year in office, Obama said yes, explaining that President Reagan met with the leader of “the evil empire” and that the whole point of diplomacy is to talk to your adversaries. Clinton quickly disagreed, saying that she favored more diplomacy, but didn’t want to hand bad actors like Venezuela’s Hugo Chavez and Iran’s Mahmoud Ahmadinejad propaganda victories.

Over the next three days, hostilities escalated. After first sending out an aide to “clarify” what he meant (a sure sign he thought he had lost the exchange), Obama decided to use the moment to reiterate his position. It’s arrogant, he said, for a U.S. president to view his presence at a meeting as a reward for good behavior, and his refusal to meet as punishment. And no matter what you do, there’s always propaganda from the other side. Hillary, sensing a chance to reinforce the experience gap, called Obama’s position “naive.”

This, in turn, gave Obama an opening to prove that he can counterpunch—something Democrats are desperate for their candidates to do more often. It was especially important for Obama to show he was not “Obambi,” and he seemed to relish the chance. But he may have overreached in referring to Hillary’s approach as “Bush-Cheney lite,” and not just because he delivered it too harshly. In 2000, John McCain ran into trouble in the critical South Carolina primary in part by comparing his opponent, Gov. George W. Bush, to President Bill Clinton, the incumbent and a loathed figure inside the GOP. The move backfired. Republican primary voters didn’t like seeing one of their own compared to the hated incumbent of the other party. Today’s Democratic primary voters no doubt feel the same.

Hillary took quiet but effective umbrage at the “Bush-Cheney lite” line and scored with a passive-aggressive shot at Obama for betraying the “politics of hope.” This was part of her strategy of trying to turn Obama into a hypocrite every time he says something critical.

In the short term, Hillary probably prevailed. She seemed calm and mature; Obama brash and too young. But this frame might not work to her benefit over time. Obama reinforced his image as a sharp break from the status quo, which Democrats want. Long after the details of this tussle have faded, that impression may linger.

On the substance, their views are almost indistinguishable. They both echo the line of John F. Kennedy (actually Ted Sorensen, now an Obama man) that “we must not negotiate out of fear—or fear to negotiate.” Hillary has said repeatedly that she would talk to adversaries, and Obama made it clear that he would do the requisite diplomatic spadework before rushing into meetings. Both would take a page from former secretary of State James Baker and open talks with Syria, Iran and other rogue states.

Not the Republican candidates. They all apparently feel Baker is wrong and Bush is right—no talks. Introducing a note of demagoguery, Romney went so far as to compare Obama to Neville Chamberlain, the British prime minister who flew to Munich in 1938 to appease Adolf Hitler. No Republicans objected. Their game—which they will play whomever the nominees turn out to be—is to position Republicans as Churchillian (Rudy Giuliani does this explicitly) and Democrats as appeasers. Munich is an old meme in American politics (Lyndon Johnson, Richard Nixon and Ronald Reagan all used it). But it is especially inappropriate today.

For starters, Chamberlain’s unforgivable mistake was not that he met with Hitler, but that he gave away Czechoslovakia to Hitler. It’s what comes out of the meeting that counts. Meeting a bad, even evil, head of state is not appeasement; it’s diplomacy. Otherwise, it’s hard to argue that Nixon and Henry Kissinger should have gone to Beijing to meet with Mao, one of the greatest mass murderers in history.

Moreover, the GOP’s Churchill infatuation ignores some inconvenient realities. For instance, The New York Times and other news organizations have quoted U.S. government sources confirming that nearly a third of the suicide bombers in Iraq are Saudis. That’s right—a lot of the guys killing our guys are, like 19 out of 20 of the hijackers on 9/11, from one of our top allies in the region. But that didn’t stop Bush from holding hands with Saudi King Abdullah at his Crawford ranch. Did the royal family send Saudi nationals to Iraq to be insurgents fighting with their fellow Sunnis? Probably not. Did they look the other way? Some U.S. officials now think so. This puts Saudi Arabia in about the same position as Iran when it comes to infiltration over the border into Iraq.

The point is, we are way past us-versus-them and good-versus-evil in the Middle East. And anyone who thinks the United States has the stature to demand that foreign leaders renounce their threatening and stupid views before meeting with us is living in a dream world.

If the next president has any sense, that person will convene a big international conference where all the parties will talk to each other—and to the United States—about how to repair some of the damage in the region. There’s a good bet that even the Israelis will show up. They now realize that all those years of not talking to the Palestinians didn’t bring them much. (Witness how often Prime Minister Olmert has met recently with Prime Minister Abbas).

Next year, the Democratic nominee will likely argue for a conference. And if he wants to win, the Republican nominee will edge in that direction. It’s not 1938 anymore. Or even 2001. After all the squabbling, the candidate who best understands that new reality will be the next president.