Federalists supported a strong central government. They wanted to give a lot of power to the national government and not a lot of power to the states. On the other hand, the antifederalist wanted to give more power to the states because they feared that giving a lot of power to the federal government would create an oppressive monarchy like the one they had just escaped after winning the Revolutionary War against Great Britain.
Because popular sovereignty was well supported because it allowed the local citizens of a territory to decide if slavery was to be allowed or illegal. Stephen A. Douglas pushed for popular sovereignty during the 1840's.