For many years I used this chart to show that the relationship between federal debt outstanding and interest rates was exactly the opposite of what most people tend to think: the two have been for the most part (with the notable exception being the 1990s) inversely correlated for many decades. That relationship may now be on the verge of changing: the big increase in federal debt that is slated for coming years will likely correspond to rising interest rates. The reason? Debt is going to be increasing much faster than GDP for years to come, and the Fed is making huge purchases of Treasury debt, thus monetizing the debt as never before.
Rising interest rates are thus likely to be driven by a) an avalanche of Treasury supply and b) rising inflation. These are going to be the critical issues to focus on in coming years. I don't think they mean that the economy will collapse. Instead, I think it is a good reason to expect that economic growth will be subpar (averaging less than 3%) for many years.