The line was designed by a Northerner - Jesse B. Thomas of Illinois.

The whole debate didn't start out with the line. The real concern in Congress was the balance of power between free states and slaves states, so the whole congressional discussion of the law was about admitting Maine and Missouri as states at the same time so that the balance would remain intact. There were several northern Congressmen who had no intention of passing a bill allowing another slave state to join the union in 1819. Most of the northern states had passed abolition acts before the turn of the century (except New Jersey). So Jesse Thomas tacked this on to make the law more attractive to northern congressmen. The original proposal, which had no mention of 36°30′N in it, had been amended twice and was dying.

Southerners were ramping up toward king cotton by this time anyway and Iowa and Kansas weren't in the cotton belt. I would imagine that Henry Clay was able to convince a lot of southerners to focus on the short term and find a compromise to avoid more political fighting, explaining that they would work out future arguments at a future time.