First, American Exceptionalism is a view, deeply ingrained in our culture, that the United States of America superior among nations as if god-given. The "Gods" in this case were the "founding fathers," and the US form of democracy is viewed as not only the best, but unsurpassable.
This notion of being "special" includes a belief that US actions are for the common good of the world. The US spreads democracy, which is a noble pursuit. It is a belief held by both conservative and liberal Americans, albeit liberals acknowledge past imperfections of slavery, the omission of women's rights in the original constitution, etc.
When it comes to foreign policy in particular, American Exceptionalism binds the Democrats and Republicans to very similar views and imperial activities abroad. Take the following doctrine for example:
Let our position be absolutely clear: An attempt by any outside force to gain control of the Persian Gulf region will be regarded as an assault on the vital interests of the United States of America, and such an assault will be repelled by any means necessary, including military force.
This policy was voiced in 1980 by President Jimmy Carter. To be even more clear, no outside force will impinge on US Control of Persian Gulf Oil... it is unstated that the "benevolent" United States should have control over this oil rather than anyone else. The establishment agrees, and American Exceptionalism is a common underpinning of that agreement.
For More on the mythology of American Exceptionalism, and its implications, check out GDAE Podcast Episode 18 (35 - min).