It is very important to note that Winthrop was not aiming to create an "America." This is teleological thinking, looking toward today. It also privileges the New England model as somehow representative of all of colonial life. As someone who studies colonial history, I would submit that the Chesapeake and the Carolinas were equally important as New England, and almost entirely different. But if we considered them, we'd have to confront our beginnings in societies based on forced labor. On the other hand, if we considered the Middle Colonies, we'd be confronted with an impossibly diverse region. Trying to divine lessons for America as a whole today from one colony in one place at one time is not good history. Good politics, maybe.
Personally, I believe this is a true statement. As a teacher, mother and Sunday School teacher, I find that all eyes are upon those who are in position to influence others. Others look to us, whether we be presidents or average "citizens" to see what we are all about. If we are in a position to set some kind of example, it is our responsibility to do so. A teacher with a mean streak can turn kids off to school and/or education. Being nice does not guarantee dedication to one's lessons, but at least students can come to class knowing that in this class, they don't have to worry about being berated or treated unfairly. In this way, kids may not like English, but they will feel safe and accepted in my class.
In terms of being a parent, if there are things I want my children to believe in or emulate, the first teacher they will have is me. If I teach them that lying and cheating are wrong, I had better be a shining example, like that city on the hill, or I'm a hypocrite and that sends a great many negative messages. It's important, too, that my children know I can make mistakes, and I would hope they can learn to forgive me, others and themselves for not being perfect. (So often peers within a school setting like to point out other students' imperfections; kids can't always see beyond the hurt to realize that those who criticize are in the same boat: imperfect.)
I guess the part about being a Sunday School teacher speaks for itself. My example is not only being studied by my kids, but by their parents. I don't worry about this too much because I try to live what I "preach," but there is perhaps nothing worse than someone who takes a moral stance and then does not abide by it. Besides misleading others, it garners a great deal of criticism for the institution (i.e., church, religion) which is not reflective of the whole.
In terms of Winthrop's allusion to the Christ's words: "We should be like a city on hill...the eyes of all people are upon us," I agree. We need to set an example. More than that, there comes a certain amount of peace in knowing not that we are perfect (we're not), but that we believe strongly in doing the right thing as best we can, and that we can offer concern and support for others. Life is complicated enough without having to worry about cheating on taxes, lying, etc.
One makes a mistake if one separates the statement from its context. Earlier in the Sermon, Winthrop had commented that they should"be as one man," they were to be an example of Christian Charity, bear each others burdens, share with each other, and be a model to the rest of the world; in fact the Sermon is entitled "A Model of Christian Charity." The Puritan Community was founded and based on religious principles. The Chesapeake Bay colonies were founded on purely economic principles. Under any circumstances, we have obviously evolved from the Puritan attitude. Winthrop's Sermon was timely and appropriate for its time and place. For today, it is as antiquated as a buggy whip.
The United States with it's (originally) pretty unique type of government has always been a model for other less enlightened countries. We must be aware and conduct business accordingly. This does mean a separation of church and state must be maintained, so even though I personally disagree with things like eliminating prayer from school, it is necessary to ensure equality. We can't address all faiths, and look at the countries that have tried to establish national religions.
Are you asking about this in the context of the Massachusetts Bay Colony, or in our own context today?
In the old context, Winthrop was saying that their colony should be an example of godly living to inspire the rest of the world. I have no problem with a society aspiring to be an inpsiration to the rest of the world, but I would not like the government to be in charge of making this happen. I think it should be left to the churches and other institutions to accomplish this.
If in today's context, I think that we should aspire to be a city on a hill, but not in the religious sense. I think the US should aspire to be a city on a hill in the sense of our civic and political values -- I think that we should try to set an example for how the rest of the world should arrange its affairs. (Of course, it would be nice if we could get our affairs in order just for our own sake...)