Actually, if you look at his plan the deficits were intended to be temporary. Get the economy expanding, then reapply taxation to stabilize growth while paying back the money that was used to establish the growth. Much like a business borrows money to get going, then uses the profits to expand further while paying down the debt.
The problem was the only person capable of following his plan through turned out to be him. When the time came GHW Bush didn't have the charisma to raise the taxes and get away with it. Then Clinton came in and enjoyed eight years of riding the exploding economy like a surfer on a hot wave and making no effort to bridle it for long term benefit whatsoever. When the wave was finally petering out GW Bush and his merry band of idiots thought they could reenergize it through the same process that made it in the first place, despite the fact they were by then standing on dry sand (in other words they did not have the existing conditions Reagan had, so trying to use the same plan made no sense whatsoever but they did it anyway).