First of all, how should the size of government be measured? There are two ways to do this, by measuring total government spending per person, or by measuring total government spending as a percentage of Gross Domestic Product (GDP). The latter methodology is essentially measuring the size of government relative to the size of the economy.
According to the Fraser Institute, “The observation that higher income countries can afford more per capita government spending limits the usefulness of per capita government spending as a measure of public sector size, making government expenditure to GDP a more suitable measure” .
For example, the US government may spend more per person than the Egyptian government, but that is simply because the US economy is so much larger than the Egyptian economy. Because of this difference, the US government is comparatively richer than the Egyptian government and can afford to spend more per person. How much the government spends per person is not an indicator of the size of government, however, total government spending as a share of the economy is. Thus, nearly all empirical research on the government measures its size as government spending as a percentage of GDP (the economy).
So, what does the empirical literature say about the size of government’s relationship to economic growth?
Building on the earlier research of James Gwartney et al. , scholars from Duke University and Wheaton college recently produced a study documenting the relationship between government size and economic growth between the years 1960 and 2010. The below graphs display their findings.
See citation #2
It is fairly obvious that the correlation between the size of government and economic growth is negative. However, this correlation does not include other control variables which may effect growth. Thus, the statistician's warning of "correlation does not prove causation" is noted. However, while this study did not include control variables, dozens of other studies have in order to isolate the effects of the size of government on economic growth. Even when controlling for other variables (such as inflation, demography, etc), the majority of research finds a strong negative correlation between the size of government and economic growth.
According to a recent survey of the academic literature on this subject published by the Research Institute for Industrial Economics:
“The most recent studies [on the relationship between government spending and economic growth] find a significant negative correlation: An increase in government size by 10 percentage points is associated with a 0.5 to 1 percent lower annual growth rate...When we singularly focus on studies that examine the correlation between growth of real gross domestic product (GDP) per capita and total government size over time in rich countries (OECD and equally rich), the research is rather close to a consensus: the correlation is negative.” 
These findings don't prove but do provide evidence in support of the idea that the negative correlation is in fact driven by government spending causing lower economic growth.
Even facing this evidence, proponents of large government may argue that the benefits of having a large government outweigh the costs of a slower economic growth rate. Here's the thing, the cost of a slower economic growth rate is tremendous and in the long run will determine whether a country is rich or poor. As economists Andreas Bergh and Magnus Henrekson have noted:
"[A]n annual growth rate of 2 percent means that the economic standard of living doubles in thirty-six years. But if the annual growth is instead 3 percent, a doubling of the standard of living takes a
mere twenty-four years." 
In order to emphasize this point, let's examine how family incomes would have grown in the absence of large government. According to a study by Gwartney et al.: "If government expenditures as a share of GDP in the United States had remained at their 1960 level, real GDP in 1996 would have been $9.16 trillion instead of $7.64 trillion, and the average income for a family of four would have been $23,440 higher." 
Based on these findings, one may ask, "what is the proper size of government?". In the economist's eyes, the proper size of government is the one which maximizes economic growth. The Rahn Curve (below) suggests that initially, government spending on public goods such as a legal system, infrastructure, and defense will cause the economy to grow faster. However, once the government starts spending too much, it will take money and resources away from more productive uses in the private sector, leading to slower economic growth.
Most empirical research finds that for the average country, the optimal size of government is no greater than 25% of GDP. Take for example, a recent study by the Institute for Market Economics, which has stated:
"The evidence indicates that the optimum size of government, e.g. the share of overall government
spending that maximizes economic growth, is no greater than 25% of GDP based on data from the OECD countries. In addition, the evidence indicates that the optimum level of government consumption on final goods and services as a share of GDP is 10.4% based on a panel data of 81 countries. However, due to model and data limitations, it is probable that the results are biased upwards, and the “true” optimum government level is even smaller than the existing empirical study indicates." 
Also, the optimal size of government for the United States may be even smaller. The Economic Inquiry has stated that, "The optimal government size is 23 percent [of GDP]... for the average country. This number, however, masks important differences across regions: estimated optimal sizes range from 14 percent (+/- 4 percent) for the average OECD country to... 16 percent (+/- 6 percent) in North America" . Currently, the size of the US government is 40% of GDP, far larger than what is predicted to be the optimal size.
In the end, it appears as though libertarians and classical liberals are right in believing that small government is much more conducive to economic growth than large ones. Additionally, these findings cast doubt on the claim that larger government is the salvation of the economy as well as of poor and working class Americans. The evidence indicates that larger government is in fact what is holding them back. While "progressives" see large government as the answer to America's problems, the reality is just the opposite. it is time to reverse the trend of growing government and restore it back to a size more in line with the intentions of the founders of our country.
 Georgios Karras, "The Optimal Government Size: Further International Evidence on the Productivity of Government Services," Economic Inquiry, Vol. 34, (April 1996), p. 2.