From another comment:

> $1M home at 3% interest(30year) = ~$4200 monthly payment. $800k home at 6% interest = $4800 monthly payment.

Over a 30 year term, your interest rate has much more impact on affordability than the purchase price does. 20% down is a drop in the bucket when your rate necessitates paying 1.5-2x the purchase price in interest because it's spread out over 30 years, especially at higher price points and at the edges of people's budgets.