The White House has survived both fire (the Brits torched it in 1814) and insults (Jefferson groused that it was 'big enough for two emperors, one Pope and the grand Lama'). Tours must be arranged in advance. Americans must apply via one of their state's members of Congress, and non-Americans must apply through either the US consulate in their home country or their country's consulate in DC. Applications are taken from 21 days to six months in advance; three months ahead is the recommended sweet spot.
If that sounds like too much work, pop into the spiffy, renovated White House Visitor Center. It's not the real deal, but hey, executive artifacts and paraphernalia are on display. Or get a view of the White House from the outside. Cars aren't allowed to pass the building on Pennsylvania Ave; you can get good photos across the North Lawn from here. Or move to E St NW and take pictures across the South Lawn.