After noting that Democrats and Republicans have different economic policies

They are actually quite similar. Spend, spend, and spend. The only difference is where they spend and how much they tax or borrow.

Most economists will also tell you that Presidents don't even control fiscal policy.

Perhaps not directly, but they appoint those that do (e.g. Ben Bernanke).

Presidents along with the legislative branch do have an effect on the value of the dollar, which does have an effect on the health of the economy. Executive and legislative branches contribute with budgets, spending, and fed appointees who make monitory policy.

Consider this:
A presidential appointee to the federal reserve, Ben Bernanke, decides to lower interest rates to "stave off inflation." When the fed reduces interest rates this reduces the value of the dollar. Why? Because U.S. Treasury bonds have a lower yield when interest rates are low. Lenders (largely foreign) are then less willing to buy Treasury Bonds at these lower rates because their return is lower. Plus the $10+ Trillion in federal debt makes them even less comfortable to buy (lend) more.

When foreign countries are not buying Treasury Bonds (lending) the fed must get money from somewhere for the spending. So they essentially have more money "created" or put into the system. The more money in the system the more the value of the dollar falls.

As the dollar falls the price of imported goods increases (we import a sh** load of stuff). When things cost more people buy less and their devalued dollar buys even less imported goods (i.e. inflation). There you have it, a worse economy is the result. Presidents, their fed appointees, and legislators have a big role in this current mess.

Data for the whole period from 1948 to 2007, during which Republicans occupied… and Democrats…show average annual growth of real gross national product…

Gross National Product (GNP) is one way of measuring the health of an economy but is less accurate now with nations increasing their production in other nations (i.e. "overseas"). A more popular measure these days is Gross Domestic Product (GDP). But even GDP is not an accurate measure of the health of an economy.

Economist Frank Shostak:

The GDP framework cannot tell us whether final goods and services that were produced during a particular period of time are a reflection of real wealth expansion, or a reflection of capital consumption. For instance, if a government embarks on the building of a pyramid, which adds absolutely nothing to the well-being of individuals, the GDP framework will regard this as economic growth. In reality, however, the building of the pyramid will divert real funding from wealth-generating activities, thereby stifling the production of wealth.

Here's a musing/question for you "right wingers":
As a reflection on GDP are U.S. wars similar to building pyramids?

Or for "the lefties":
As a reflection on GDP would social programs be similar to building pyramids?

Data for the whole period from 1948 to 2007, during which Republicans occupied the White House for 34 years and Democrats for 26, show average annual growth of real gross national product of 1.64 percent per capita under Republican presidents versus 2.78 percent under Democrats.

[Blinder]

For instance, if you lag the per capita GDP results by two years — not a bad guess of how long it takes policy to show up in output — the difference between Democratic and Republican presidencies vanishes (both are 2.2%). And if we look at it terms of government control — that is, party control of both the presidency and both houses of congress — then the Democrats do worse than the Republicans (2.0% versus 2.1%). But wait! Divided government, when no party controls both the presidency and the congress, does even better: 2.3%!

[Don Luskin again]

Please re-learn policy implementation lag, Mr. Blinder.