When Does the Film "1776" (1972) Take Place?

"1776" is a historical fiction film musical written by Peter Stone [adapting "1776" (1969) by Peter Stone with Sherman Edwards] and released November 17th, 1972. 

It takes place in the year: 

1776 AD 

We know this because (besides the year merely being in the title) it depicts proceedings during the later months of the First Session of the famous American Second Continental Congress, which lasted from May 10th, 1775 AD to December 12th, 1776 AD. It's specifically named early in the movie: "Second Continental Congress meeting in the city of Philadelphia is now in session. 7 June 1776. The three hundred and eightieth meeting." 

At the start of the second song, “Piddle, Twiddle, and Resolve”, the real-world delegate from Massachusetts John Adams sings “for one solid year / they have been sitting here! / A whole year!” The American Second Continental Congress opened in May of 1775 AD. So it's at least May of 1776 AD at the very beginning. 

1775 + 1 = 1776. 

We even know the exact day, because during and just before the first song, "Sit Down, John" (the start of act 1), a huge calendar can be seen clearly in the background that reads: "May 8". 

In the fifth song, "But, Mr. Adams", an argument is heard between the members of the real-world Committee of Five, a small group of five pro-independence members officially tasked with writing a declaration of a list of reasons to separate from the sovereignty of Great Britain under King George III. So the audience is brought to June of 1776 AD. Again, some exact days are clear as before the Lee Resolution for Independence is proposed and the Committee is appointed, Andrew McNair, the congressional custodian, is seen changing the massive calendar to "June 7". The group was brought together on June 11th, in the real world. 

The document later known as the Declaration of Independence was brought to the full Second Continental Congress on June 28th in the real world and the enormous calendar accurately reads "June 28" in the film. The tenth song, "The Egg", is sung while the document is read aloud. 

In the real world, there was debate on July 3rd about an anti-slavery section in the document the Committee of Five produced. The eleventh song of the movie, "Molasses to Rum", is a reminder from the real-world representative of South Carolina, Edward Rutledge to the Northern colonies' delegates that their homes are equal beneficiaries of the "triangle trade", which included slavery. The story moves the final real-world removing of this passage on July 3rd a day backward, to July 2nd. 

Finally, the narrative ends with the famous real-world ratifying and signing of the United States of America (then the United Colonies) Declaration of Independence on the late morning of July 4th during the final song, "Finale". The film combines this moment with the real-world earlier vote on the key part of the Lee Resolution for Independence on July 2nd, which marked the group's decision to declare the United Colonies a new nation. It also should be noted that scholars now believe, while the ratification of the Declaration happened on July 4th, the full signing by all participants present actually occurred with a fresh copy on August 2nd. Essentially, these three dates' events (July 2nd, July 4th, and August 2nd) are all condensed to July 4th, 1776 AD for a dramatic conclusion.