Portraying economists as falling in each of these two camps is an oversimplification. Most economists in the profession recognize the important of structural reforms and improving the supply side of an economy. In fact, all economists I can think of when they write or teach about growth in the long term they talk about how a country can improve its productivity, effort, capital stock, all of them variables that are associated to the supply side of an economy (the assumption is that demand adjusts at the same time as production feeds into income and then expenditures).
What I find interesting is that the consensus that supply (incentives, productivity, innovation) drives output and welfare in the long run is then used in the political debate to push the argument that small governments and low taxes are the only sensible economic policy (at any point in time). And any argument in favor of higher taxes or a stronger roles for governments is dismissed on the grounds that it will create massive distortions and low growth.
Best way to find the extreme use of this simplifying argument is the definition of "Supply-Side Economics" that one can find at the Laffer Center (for Supply-Side Economics):
"Supply-side economics emphasizes economic growth.."So far so good, we all like higher economic growth
"...achieved by tax and fiscal policy that creates incentives to produce goods and services." In particular, supply-side economics has focused primarily on lowering marginal tax rates with the purpose of increasing the after-tax rate of return from work and investment, which result in increases in supply. The broader supply-side policy mix points to the importance of sound money; free trade; less regulation; low, flat-rate taxes; and spending restraint, as the keys to real economic growth. These ideas are grounded in a classical economic analysis that understands that people adjust their behavior when the incentives change. Accordingly, the lower the regulatory and trade barriers, and the lower and flatter the tax rate, the greater the incentive to produce."Why the focus on tax and fiscal policy or marginal tax rates or restrained spending? What about other institutions, rules, incentives that can affect growth? What is surprising is that the academic literature that has explored the determinants of economic growth finds limited support for many of these variables as key determinants of differences in growth rates across countries. Other things such as investment, education or innovation matter much more. And while one can argue that these variables themselves could be ultimately driven by taxes, the evidence is once again very weak on inexistent.
The point is not that taxes do not matter when it comes to economic growth but that the oversimplification that makes supply side = small governments and low taxes seems to miss many of the variables that the academic literature identifies as determinants of growth, some of which could require a larger and not a smaller role for governments and regulation.