We've had this discussion already. SOme of us would get excited and pee on the floor, and others would abandon our homes and climb the highest rock and wait for salvation. But the other 99.99999% of us would go on about our lives.

If the US government found some artifact, they might well keep it quiet, but to be fair to the OP, let us assume some sort of auromatic probe from a distant place far away and from long ago landed itself in Yellowstone, or Times Square, or in front of the Dallas Book Depository. Some evidence that couldn't be kept secret. The question is what would the general public do if the general public became aware there was ET out there somewhere.

"Hey, Hon, paper says here that an alien spaceship landed downtown."
"Yeah, well, is that alien spaceship gonna take out the trash and mow the lawn? Get off your butt and get 'er done."

Later at the bowling alley, "Hey guys, look. There's an alien spacship landed downtown."
"Yeah, right, you're up, grab the ball and bowl."

"We interrupt this broadcast of the National Football League playoffs to present this important bulletin: alien spaceship just landed downtown."
Eighteen million TV sets explode simultaneously as bricks are thrown at them.

The public won't care. Since half of them already believe ther are aliens out there, this is not news. To those who find it novel, many will find it yet another way for the government to waste our money. Right wing whackos will buy extra ammo on the way home from work, and call their friends to reinfore each other's belief in the conspiracy of the government not telling the whole story. KAtie COuric wil ask the family whose car was crushed how it feels to have their car crushed and will they be devastated because the dog was still in the car?

"Hey, Hon, says here there's an alien spaceship landed downtown."
"Well, Duh, they been seeing those UFOs all over for a long time. Bout time they figured out what it was."

Local News will have a story or two, for a day or two. Roast beef will still be on sale all week at Kroger. The new Buick for 2007 will come out in the fall. AMtrak will lose money. Baseball will go on in the spring, and people will argue about player salaries - a lot more than they will about the alien space probe.