Just create a Date object from it and do .getTime() or use Date.parse():

var d = new Date(Wed Jun 20 19:20:44 +0000 2012);

d.getTime(); //returns 1340220044000



//OR



Date.parse(Wed Jun 20 19:20:44 +0000 2012); //returns 1340220044000

Works great if your human time string is in a format that the Date constructor understands (which the example you posted is).

EDIT

Realized you may mean a Unix timestamp, which is seconds passed since the epoch (not ms like JS timestamps). In that case simply divide the JS timestamp by 1000:

//if you want to truncate ms instead of rounding just use Math.floor()

Math.round(Date.parse(Wed Jun 20 19:20:44 +0000 2012) / 1000); //returns 1340220044