At the end of Bill Clinton's presidency we were paying down the national debt so fast that the Congressional Budget Office estimated the entire public debt would be paid off in as little as 10 years, for the first time in American history. George W Bush put a stop to that with two rounds of tax cuts (even he reportedly asked Cheney why they were doing the second one), by exploding spending on two wars, and by introducing a Medicare drug benefit mainly financed by massive borrowing.
Prior to Clinton, the last president to produce a budget that reduced the debt was Lyndon Johnson -- at the height of the War in Vietnam, the War on Poverty, and the Apollo program, not to mention the launch of Medicare and Medicaid.
The most important number is the ratio of debt to the economy. We came out of World War II with a public debt substantially bigger than annual GDP, but that ratio came down under every president from Truman through Carter except Gerald Ford; during his brief term it stayed roughly level. When Reagan took office the public debt been cut to under a third of GDP. But under Reagan and Bush 41 it rose rapidly, declined under Clinton, and then shot up again under Bush 43 and Obama, in the latter case largely as a consequence of Bush's wars and digging out of the Great Recession.
We should reduce our debt-to-GDP ratio, but it's not a crisis and debt in itself isn't inherently bad -- it's not crazy to take out a mortgage, and many well-run, successful businesses issue corporate bonds. Right now the annual deficit relative to the economy is lower than the average for the past 50 years, and with interest rates near zero in real terms we can easily afford to service the debt. Looking at the big picture, we'd actually be better off investing in our infrastructure in the near term, then paying down the debt over a longer time frame.
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