Perfect soundtrack to this post...
Even though today's looming government shutdown of nonessential services might demonstrate the more extreme consequences of a government in a budget crisis, this is not the norm, nor does it really infringe on the essential functions and services of government. A government shutdown is an attempt to deal with one of the most expensive line items of that budget - labor costs. Things like regulations, entitlements, and the military will not suddenly disappear just because the government - at this moment in time - does not have the legislative ability to fund them.
So, extremes aside, how should the government attempt to provide service to a growing demand base, when budgets are held to current levels, or even decreased?
First, take the entitlement debate out of the equation. This is difficult, since a majority of the government's budget is spent on social security, medicare, and medicaid, but nonetheless necessary. Entitlements are not a budgetary issue, they are an issue of rights. Plus, you can find tons of scary charts like the one below from the GAO that just tend to confuse the issue and send people into a panic. The federal government does not have the ability to tinker with these numbers without upending fifty years of SCOTUS precedent, so until some systemic reform is able to occur at some isolated future point (not in the rush of annual budget approvals) there's no use talking about it.
Second, inform citizens on how much the government is spending and what it's spending it on. If your citizenry believes you are spending way too much on the wrong things then any kind of serious national discussion will be difficult. For example, in a poll by CNN, American's allegedly believe that CPB & NPR receive 5% of the federal budget, a whopping 178 billion dollars, when in actuality they receive about 430 million a year.
Third, ask citizens to prioritize what services they simply can't do without. The UK's attempt at doing this is a good start.
Fourth, outsource. Government has the ability to galvanize an economy like few other things can. People need government services when they don't have a job and need assistance. Use government resources to boost the private sector to employ citizens in small firms for IT support, procurement, bidding, office supplies, etc. Small firms are the quickest way to spur greater entrepreneurial activity and market dynamism which leads to growth.
Fifth, when you have to start cutting, don't go for the easy targets. Things like social programs, programs that help others abroad, and aid to states.
Sixth, reign in tax loopholes like the mortgage interest deduction which typically doesn't greatly increase the rate of home ownership and just enables middle and high income households to get their homes (that they would buy anyway) either cheaper, or larger (that latter which is of course an environmental concern).