It would be insane to try to pay off the national debt. It happened once and it was a disaster.
The Panic of 1837 was unrelated to the temporary elimination of the national debt in 1835. Not that government policies weren't a factor, but the brief lack of a national debt wasn't one of them. Rather it was the Specie Circular and the replacement of the Bank of the United States with the pet banks that were the major governmental factors, but neither of those were related to the elimination of the national debt.