People are pretty polarized as is. Otherwise, there won’t be controversial issues, right? Sometimes, deliberation, if the time frame is too short, it brings out the worst of people. It’s true. It happens.
By declaring, "We won’t conclude this stage until we reach a super-majority consensus feeling," we are basically say, "OK, keep debating until you come up with something that you all came to agree with." That solves the problem.
Most of the pressure is created by a fixed time frame, or by an overly broad subject in which no overlapping consensus is possible. If you narrowed the issue enough, and then provide a long enough time — more than three or four weeks — then inevitably, they come to converge.