In a practical sense, a deficit is bad because it represents overspending. The government has taken on so many future liabilities to pay for present goodies that we're worried about both: the government defaulting (meaning it can't pay the interest on its debt), or the increased taxes required to pay the debt strangling growth. Both are very bad.
Excessive borrowing typically affects exchange rates, which makes it more expensive to import things, and reduces consumption. Excessive borrowing will also typically raise interest rates for borrowing, which is bad should an emergency arise (a real war) or default loom. Borrowing may make spending too easy, and since the politicians aren't spending their own money, the outcry over deficits may be a kind of constraint - though it hasn't been very good.
In an abstract sense, I think too much government spending is bad - it distorts individual decisions in the market, it deprives people of stuff they actually want, and could trigger any of the problems above. But short of excessive borrowing, deficits/debts really don't matter much by themselves - the spending decisions are the real issue.
As a means of explanation, let me give you an example swiped from Steven Landsburg. In the example, you want to buy something. It costs $100 and the interest rate is 10%. You happen to just have $1000 in your bank account. You have three ways to fund your purchase:
1. Buy it outright. $1000 - $100, plus $90 in interest = net assets of $990
2. Buy it on credit and pay it back a year from now. $1000 + $100 in interest - total costs of $110 (principle + interest), net assets = $990
3. Buy it and never pay for it outright. Eternal deficit. At the end of the year you have $1100, you pay the interest of $10 and you never pay the principle. But you don't have $1090 left, there is $100 you can't spend so you can be sure you can afford the interest each year. So you have usable assets of $990.
All three end up exactly the same. The issue we ought to concern ourselves with whether or not to spend the $100 in the first place, NOT how to finance the spending. To make this crystal clear, if the US Government had large opportunities to invest that would bring in more than they cost, would anyone be upset by the deficit used to fund these opportunities? Obviously that isn't the case now, which is why it is so important to scrutinize what we're spending money on rather than just how much.
Now let me address a few criticisms of this general idea. You can argue lending interest rates aren't equal to saving interest rates. But for the government the two rates are really close.* You may argue we don't have the $1000 in the bank to begin with either, but this result doesn't flow from whether or not we have the money in the bank - so long as we have $10 of sure income each year, we can take option 3 and the total cost is just the same as if we chose option 1.
We always say deficits are burdens to the future. But that's only half of the story. Interest payments on past debt are offset by the interest we earn when we defer our tax liability. Government borrowing allows us to defer paying our taxes, but it also allows us to earn extra income from the additional assets we've retained/created. The future inherits our assets as well as our debts, and so far every generation has been richer than the previous one (though of course past results don't guarantee future performance).
Hopefully verbosity hasn't obscured my point. My tl;dr is this: we should be careful about where the government spends money. If we can fix the spending problem, the financing problem falls in line.
* Obviously the government can't stick money into a savings account, or the stock market, or the normal investment vehicles we use. I do think federal or state governments can earn a normal rate of return by investing in assets that add value to the economy or buying bonds from other governments. I think rates on those investments can be comparable to debt rates.