Did they see it as prosperous, like Europe, or something completely different?
Sorry for taking so long to get to this!
Of course, "people" is a tricky word. A slave in South Carolina likely had a different outlook on the world than a Boston merchant. "Colonial America" is also tricky - Ask a slave and a trader this question in 1740, and they'll give you very different answers than the ones they might give in 1780.
So, to focus on one particular person and one particular moment in time, I present to you Information to Those Who Would Remove to America, written by Ben Franklin near the conclusion of the Revolutionary War. In it, Franklin paints a pretty rosy view of America. He envisions an expanding republic, populated by hard-working farmers and tradesmen. European immigrants would be welcomed, but only if they left behind their ancient prejudices and belief in titles. Even aristocratic immigrants, in Franklin's ideal, would be respected only as much as the quality of their work warranted. Franklin also sees work as an essentially private enterprise: he does not envision America having a particularly large civil service or military, two major sources of employment in Europe.
Let me know if I can address more specific parts of your question!