Reagan ended up raising taxes because the economy was in the pits for his first two years. The Federal Reserve had been tightening money since October, 1979. That was what pushed the economy into recession in 1981, which cost Jimmy Carter his job. These tight money policies created a crisis for the Mexican peso, forcing it way down, thereby increasing its dollar-denominated debt burden. In the summer of 1982, Mexico responded by nationalizing the banks and threatening to default on its debt.
The FED started pumping money, and it has not looked back.
Then Reagan hiked Social Security taxes in 1983 because the system had technically gone bankrupt: more outflow than income.
Reagan ran enormous deficits throughout his time in office – the largest in peacetime American history. This was Keynesianism, but it was called supply-side economics, even by supply-siders.