It's been estimated that launching material on the space shuttle costs about $10,000/pound ($22,000/kg). Even if engineers could bring down prices by a factor of 10, it would still be thousands of dollars to launch the garbage into space. Let's imagine a wonderful dream world, where launch costs could be brought down to $1,000/kg - a factor of 1/20th the cost to launch on the space shuttle.
It has also been estimated that the United States alone produces 208 million metric tonnes of garbage per day… per day! So, to launch all that trash into space would cost the United States $208 billion per day
… per day!