Judging by the rapturous reception at the Republican National Convention last night, former Secretary of State Condoleezza Rice might be considering a future in politics.

Certainly the Twittersphere was bubbling with suggestions that Rice was a potential presidential contender after she spoke movingly about overcoming racial segregation in Jim Crow Birmingham. Recalling those days, she said, “Her parents can’t take her to a movie theater or a restaurant, but they make her believe that even though she can’t have a hamburger at the Woolworth’s lunch counter, she can be president of the United States. And she becomes the secretary of State.”

The presidential reference was obviously not accidental, and the delegates knew it.

But Rice will have to do more than make a well-received speech before running on the Republican ticket in 2016 or 2020. And it’s hard to see how a woman who has never run for elected office can escape the toxic legacy of the Bush administration in which she played a crucial role.

She had a few killer quotes in her speech last night, notably when she said that “we cannot be reluctant to lead, and we cannot lead from behind.”

She talked about the Arab Spring, and about the dictators in Iran and Syria who butcher their people and threaten regional security. But she didn’t say what should be done about it. When Rice was a member of the Bush administration, not only was she an architect of the Iraq war that saddled a generation with debt, but she encouraged Egyptian President Hosni Mubarak to democratize, then pulled back after the Islamist Hamas movement won a democratic election in Gaza.

All this was conveniently forgotten in her speech. She never explicitly mentioned the Iraq war. So before the Republicans get out the “Condi for President” bumper stickers, they’d better remember that the world of politics is a whole lot tougher than the halls of academe.