According to Pew Research promoting democracy abroad is not afforded a high priority by the American public. Not a big surprise.
What is a bit surprising is the meme that's taken hold that somehow the protests in Egypt "prove" Bush was right about the importance of democracy promotion in the Middle East. It's surprising because, despite a few speeches, the Bush administration didn't do much to further democracy in the Middle East. (Did they condition aid to Egypt, Jordan, Saudi Arabia, etc. on that basis?) It's also strange because the Bush administration's true foreign policy legacy was the notion that the U.S. was justified in preemptively attacking countries on the basis of perceived threat, whether or not the threat had fully materialized. If the administration had a "big idea" with momentous consequences for its foreign policy, that was it.
Democracy as such only entered into the public discussion in a big way when the administration was casting about for a rational to continue nation-building in Iraq. It's true that, rhetorically, the administration did diagnose many of the ills that plagued the Middle East and occasionally took some blame upon itself for those ills. But giving a speech about the importance of democracy rather pales in comparison to invading a country on the basis of preemptive defense. If Bush administration officials are looking for vindication for their boss' foreign policy doctrine as it was practiced as opposed to how it was preached, it won't be found in Tahir Square but wherever those stockpiles of WMD went hiding.