Unless the name of the country is Japan, this is what usually happens:
1) Long term interest rates go up and then gradually disappear. In other words, in an American context, the government "refuses" to issue 30 year bonds at a rate it considers "exorbitant," which means the next long maturity (say, 20 years) becomes the longest one. The process continues (unless the problem is brought under control) until most of the debt is between 1-day and 1-year.
2) Banks, and other private entities are first cajoled, then forced, to buy at every auction.
3) Borrowing costs go up for everyone since the government actively competes for funds ("crowding out"). For many, there are no loans at any price.
4) Inflation goes up even in the face of lower or negative growth since the higher cost of borrowing impairs production and the supply of goods.
5) All monetary policy becomes stop/go as attempts to control the problem through higher short term rates slow down the economy.
6) The exchange rate, up until now ignored by the Central Bank, becomes a critical variable. A lower currency, other things being equal, stimulates the economy but may discourage foreign inflows and drive rates higher. The result, usually, is an unstable currency with higher rates.
7) Equities go DOWN as P/Es' contract to match higher rates in competing investments and production loans.
8) Profitability suffers as resources are diverted from production to financial management.
The counter example is Japan where they have successfully managed to double the sovereign debt without, yet, paying the price of much higher interest rates. Which of the two cases is a better fit for the US is up to you. I for one am not happy to see the backup in interest rates.