Can the Government step in, to ban bitcoins? The price of bitcoins increase with demand. Demand increases because people can spend the bitcoins. I think the price of bitcoins started as a drug money. The main advantage of bitcoins is that the sender or buyer is anonymous.
However that does not cause the increase in demand to what it is now.
I believe the current demand is increasing as more people are accepting bitcoins, and seeing this, more people are buying it.

If the government makes bitcoins illegal, people would loose trust in the bitcoins and the prices will go down.
Cant this cause the prices to go down?
I think that banning bitcoins and enforcing the ban would be a huge endeavor. It would be expensive and probably politically unpopular. See this question: How much would it cost for a government to undermine Bitcoins? Also see What methods could a government use to shutdown Bitcoin?