Since the Constitutional Convention that created the United States of America, the Federal Government has become far more powerful in just about every sense. The government started quite weak, with little revenue and a small administrative force. This post explains how we got to a government that reaches into most of the events of our day to day lives.
There are several limitations on Federal power. Primarily, they are: the Constitution, (especially the Bill of Rights), money, technology and manpower. No matter how badly the early Federal Government would have wanted to regulate the quality of the air, food, or water, it was impossible from a purely logistical standpoint. There wasn't nearly enough revenue to employ the people necessary to monitor or enforce the regulation, and there weren't the necessary technology to perform the tests. Additionally, there was a cultural resistance to Federal powers, one that still exists today, but it is not nearly as strong or pure.
What has changed since 1787?
First of all, there have been 17 more amendments to the Constitution. The Fourteenth Amendment in particular grants vast powers to the Congress. The Sixteenth Amendment created the Federal Income Tax, which provided the money necessary to enforce more sweeping powers.
Even without these Amendments, however, the Federal Government would still have far more power today than it did in 1800, thanks to the growth of Interstate Commerce. The Constitution empowers the Congress to regulate Interstate Commerce with no specific limitations on its scope. In George Washington's time, there were no American Corporations that spanned the world. Today, most of the things that go on in our economy go through an interstate company. Republicans who want to drag the United States back to 1900 (something I've seriously heard proposed), forget the way that this expansion of power is completely constitutional, not just a Federal power grab.
There has also been a cultural change in America, especially in the period from 1901-1950. It turns out that the Federal Government is the best unit to service a welfare state*. To be honest, I don't see the Constitutional justification for Social Security, but I do see its enormous benefits. Before FDR, the elderly were the worst demographic for poverty in the United States. Social Security and Medicare have done uncountable good in improving the lives of what were once our most vulnerable citizens.
The Federal Government is also the only place that we can create useful environmental regulation. Air and Water aren't limited to a single state, only Interstate authority is appropriate to regulate it.
*It's remarkable Republicans have made "welfare" into a dirty word; the Federal Government is supposed to "promote the general welfare", it's right there in the Constitution!