Our government seems to be in a perpetual state of being in debt, and it isn't like to change.
Most likely no, it will never come to pass that either the US government will ever be debt free. There is no real incentive for them to eliminate all debt, and there is significant demand for government debt.
It's easiest to think of it like a business (governments are not businesses ), the mechanics of it are similar.
I'm going to focus on the US but most government debt is in the form of government treasury bonds. These bonds are bought by citizens and companies as a form of investments because they are a very safe investment. The first step in eliminating a nations debt would be to stop issuing new debt. This means no more bonds to invest in.
The next step would be to look at what the borrowed money is used for. The answer is pretty much anything. Highways, dams, military equipment, payroll, etc... In order to eliminate our debt, we would have to at least balance total government income with total government spending. This makes large scale spending projects much more challenging.
All this assumes that the government doesn't just "print" its way out of debt. This strategy would lead to high inflation rates, which could hurt everyone. They exist to improve the public well being.
If they were turning a profit, they would be taking more money than necessary, and not providing people with any benefit from that excess.
Ideally, a government would break even. This is a hard target to hit. The next best thing is to have a deficit. There can be some disadvantages if later generations end up with a larger burden of that debt.
However, generally later generations benefit from having better schools, healthcare, and transportation options as a result of government spending.
The only time debt is bad for a government is when it can't be paid. This gives the government a lower credit rating, which means higher interest rates. That bridge that the government wants to build now costs a couple extra million in interest.
But the bridge is no better because of that interest.
The only difference is that the people who loaned the money are taking a larger risk, so will get more money back in return provided the government continues to pay its debt.