The draft continued despite the fact that congress never officially declared war
Charisma and propaganda--Reagan knew how to reach his audience and convince the American people they were in a state of danger and he had been able to keep them safe.
The Reagan administration focused on Cold War tactics first convincing American citizens they were unsafe in a world with communism and the USSR. He then developed military focus and propaganda to prove his leadership was keeping Americans safe. This with large tax breaks and a sense of conservative 'normalcy' made him very popular with the majority of white America.
The strongest supporters were the Antifederalists. Hope that helps out.