Some of the same ideals were present. The difference was that the revolution was fought on faith and hope that the new country could come to be, and everyone bound together to make if happen. The writing of the constitution was different both because they had already succeeded, and because now they were not all working for one another. Individual state interests, personality conflicts and hubris were now the rule.

I assume you mean the Civil War as the Second American Revolution, although some have referred to the War of 1812 as a second revolution too, or the war for economic independence.

The idea of self-government, sovereignty, and democracy that is closest to the states and people are similar ideals found in both the Revolution and the secession of the states during the Civil War.  In both cases, those who rebelled were acting against what they believed to be a distant, tyrannical government that did not have their best interests at heart.

As an important piece of evidence to back that assertion up, remember that the Constitution of the Confederate States of America was nearly identical to that of the United States of America.  It contained a line item veto and constitutional guarantees of the right to own slaves, but that was essentially the whole difference.

The ideals of the American Revolution were truly "revolutionary." This is because common people were motivated to take up arms against what they considered to be oppressive government; as outlined in the Declaration of Independence by Thomas Jefferson. American colonists considered themselves to be acting upon and defending their natural born rights as outlined in the English Bill of Rights; therefore they were justified in their actions to rebel. The second revolution of sorts was creation in implementation of the United States' second government; the Constitution. The first government, the Articles of Confederation, were, in simplistic terms, a group of intentionally powerless representatives. This intentional powerlessness led to the Philadelphia Convention and ultimately gave rise to your second revolution. A powerful national government, containing checks and balances, etc. The real revolutionary success of the Constitution actually comes in the aftermath of George Washington's two terms. Events such as the creation of a national bank, the Whiskey Rebellion, etc. managed to prove the success of the young nation to govern itself. It, however, would have to win a second war with England before it could prove itself worthy of respect on a world wide scale.

The ideals of the Revolutionary War, as embodied in documents such as the Declaration of Independence and Thomas Paine's Common Sense were much more radical and democratic than the ideals of the Constitution.

At the time of the Revolution, the leaders of the rebellion (mainly colonial elites) needed to gain the support of the common people.  For that reason, they started to pitch the rebellion as a fight for democracy and equality against monarchy and privilege.  Once it came time to govern their new-won country, however, this idea of democracy and equality did not seem as appealing.

Many of the Framers of the Constitution believed, like Alexander Hamilton did, that the mass of the people were too ignorant to govern themselves well.  They believed that an educated and superior elite should have the bulk of power.  Because of this, they set up a new Constitution that took much power from the people and insulated it (President, Supreme Court, and Senate not elected by the people for example).

This idea of insulating power from the people was much more conservative than the more radical ideals of the Revolution.