It's important to note that Thomas Paine was a fairly prolific writer, in the sense that he published ideas on everything from the rights of women, slavery, the colonies, and more.
That said, John Adams in 1805 (he was president until 1800) wrote that he "...[knows] not whether any man in the world has had more influence on its inhabitants or affairs for the last thirty years than Tom Paine."
However, it wasn't all cheery for his reception of course. Originally, it's usually said that Paine wrote "The Rights of Man" as a response to an attack on the French Revolution by Edmund Burke. In that regard, it was meant to be a defense of the Revolution, but that was not received well for two reasons:
The French Revolution became more and more violent, and began to represent a challenge to established order.
It was also seen as a vigorous attack on the British system of government, which meant it provoked outrage from American and British conservatives alike.
As Boller puts it:
After publication of Rights of Man, a storm of critical books, articles, and pamphlets descended on Paine and he was charged with everything ranging from ignorance, mendacity, and vulgarity on the one hand to recklessness, demagoguery, and downright anarchism on the other. Even people who sympathized in part with his views were offended by his loud strictures on the British form of government.
However, many of the most fervent critics were just supporters of Burke, and in the United States he remained very popular overall. Until he published what was seen as an attack on orthodox Christianity in 1794, and an attack on George Washington in 1796, Americans viewed his ideas mostly tastefully, and liked the "natural rights" argument he took with these things.
The reaction began to vary, over time. Social darwinists after the Civil War, and slavery apologists before it, viewed Paine's "natural rights" ideas with mostly contempt. They regarded those ideas as sentimental myths that were good for getting people mobilized to fight tyranny, but were definitely not true.
John Keane, a political theorist, put it this way: "Paine swam comfortably in the Cosmopolitan waters of the Enlightenment". He was almost always at the forefront of issues that were "progressive" for his day.
Thing is, while people loved Paine and most of his ideas, it seems that most also chose to divorce his welfare suggestions from his rights suggestions. Where people did choose to acknowledge his welfare suggestions, they also seemed to shove them aside, making them " plan for the future" rather than something to be dealt with now. And again, because those suggestions came on the heels of criticisms of British government systems, the reaction didn't lend itself to any real changes...it merely laid the groundwork for later discussions of rights, and got people thinking.
Sources:
From Liberalism to Radicalism: Tom Paine's Rights of Man Gary Kates Journal of the History of Ideas, Vol. 50, No. 4 (Oct. - Dec., 1989), pp. 569-587
Thomas Paine and Natural Rights: A Reconsideration Paul F. Boller Social Science, Vol. 52, No. 2 (SPRING 1977), pp. 67-72
Tom Paine: Utopian? Mark Jendrysik Utopian Studies, Vol. 18, No. 2 (2007), pp. 139-157