Actually, the question is really more about the growth rate of the deficit, not if there is one at all. To illustrate using a household model, if you make $100/year and you have a debt of $80 you have a debt of 80% of your "GDP" (analogy - not perfect, but right idea). Now, if you run a deficit that increases by 10% per year and you expect your intake to increase by 5% per year, then you have a long term debt crisis, since your debt will grow relative to your GDP every year (e.g. after year 1, Income of $105, Debt of $88; after year 2 Income of $110.2, Debt of 96.8; in 30 years, you'd have debt running at 325% of GDP - and a failed economy 15 or 20 years ago).
However, lets say your model expect that you will continue to run a constant deficit of $5 and expect an income growth rate of 5%, now you have a high debt-to-GDP ratio in the short term, but even if you continue to deficit spend at this rate, you have no long term debt crisis. In this model, over time, your GDP growth will outstrip your Debt, so while debt will continue to rise, it will shrink as a percentage of GDP, which is the relevant factor. (In this specific case, your Debt:GDP ratio would grow for a bit peaking in year 4 or 5, but then begin to fall off and by year 30, you'd have a Debt:GDP ratio around 55%. Keeping it up for 100 years would reduce your debt to 4.5% of GDP - so long term you are fine so long as you have the cashflow to meet your short and medium term obligations.)
Bottom line, you don't have to eliminate deficit spending, you just have to control it so that, in the aggregate, it grows more slowly than GDP.