Is modern American culture an outgrowth of the philosophies of the Founding Fathers? To what degree? How can I use these sources to make an argument? The sources are The Declaration of Independence, Speech to the Virginia Convention, The Crisis, Poor Richard's Almanac, and All I Really Need to know I Learned in Kindergarten.

Modern American culture is still an outgrowth of the philosophies of the Founding Fathers because we still believe in their idea that Americans should enjoy liberty, and we still believe in their faith in hard work and in their idea of American exceptionalism. The Founding Fathers instilled in Americans the idea that liberty is of paramount importance--though, at first, this liberty was extended only to white men. Jefferson's Declaration of Independence spoke of the rights of "life, liberty, and the pursuit of happiness." Henry's speech to the Virginia Convention referred to the conflict with the British king over taxation without representation as "nothing less than a question of freedom or slavery." In Paine's article in The Crisis of December 23, 1776, he wrote the following:

"Whether the independence of the continent was declared too soon, or delayed too long, I will not now enter into as an argument; my own simple opinion is, that had it been eight months earlier, it would have been much better."

In other words, the Founding Fathers believed liberty was a fundamental right, though it was not extended at that time to slaves, women, Native Americans, or people without property. The idea of personal liberty is still an American value that is pervasive in our culture.
Another value that the Founding Fathers gave to American culture was that hard work can bring about one's triumph. Paine wrote in The Crisis, "yet we have this consolation with us, that the harder the conflict, the more glorious the triumph." In other words, the difficulty of the Revolution would make the American victory more precious. Franklin's Poor Richard's Almanac also extols the value of hard work and implies that anyone can become rich in America through this type of hard work. Fulghum's All I Really Need to Know I Learned in Kindergarten is a modern-day work that extols some of the same values of hard work, including the following:

“It’s the spirit here that counts. The time may be long, the vehicle may be strange or unexpected. But if the dream is held close to the heart, and imagination is applied to what there is close at hand, everything is still possible.” 

In other words, Americans believe that anything is possible through hard work and that one's dreams can become a reality. 
The Founding Fathers also gave us the idea of American exceptionalism, the idea that America has a special place in the world. Paine wrote in The Crisis:

"God Almighty will not give up a people to military destruction, or leave them unsupportedly to perish, who have so earnestly and so repeatedly sought to avoid the calamities of war, by every decent method which wisdom could invent."

His idea was that God ordained the greatness of the new country, a sentiment echoed in the following excerpt from the Declaration of Independence: 

"We, therefore, the Representatives of the united States of America, in General Congress, Assembled, appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name, and by Authority of the good People of these Colonies, solemnly publish and declare, That these united Colonies are, and of Right ought to be Free and Independent States."

Jefferson implied that God had blessed America's break with England. Patrick Henry said in his speech to the Virginia Convention:

"Should I keep back my opinions at such a time, through fear of giving offence, I should consider myself as guilty of treason towards my country, and of an act of disloyalty toward the majesty of heaven, which I revere above all earthly kings."

The Founding Fathers had the idea that God had blessed the destiny of America and that we had a special destiny unlike those of other countries, an idea that still prevails in our country.