Unlike the Founders, the Church Fathers did not themselves write the Scriptures. The Scriptures were inspired by the Holy Spirit and written by those with a prophetic gift. Even the earliest of the Early Church Fathers we have were probably pretty young when the Scriptures were written. Furthermore, the writings of the earliest of the Early Church Fathers never explicitly purport to provide any insight into what was meant by the text as written. There is not a body of literature contemporary to the writing of the New Testament, parallel to the Federalist Papers (for example), to which we can appeal for documentation regarding why things in Scripture were probably written the way they were written.
In fact, most of the church fathers were separated as far as we are (or farther than we are) from the Founders. Thus, their value in a grammatical-historical model of interpretation is quite dilute. They may be useful in helping us confirm that we're still reading Greek in about the same way as they did, but folks like Augustine and his contemporaries didn't have any first hand, or even second or third hand knowledge of the apostles and evangelists, much less of Moses, David, and the prophets.
Additionally, the Bible is perfect. It is a complete document that will accomplish exactly what God intended it to do. Those tasks include communicating the way of salvation and thoroughly furnishing the man of God for every good work. The US Constitution is an impressive document, but it is far from perfect. We don't even have a reason to think it would be perfect. It's a merely human work, and humans make mistakes. There is no guarantee that it will accomplish all its authors intended.
Similarly, the Bible is perspicuous. By contrast, there is no doctrine of the perspicuity of the US Constitution. Even on important points, it is possible for the US Constitution to be vague. Just as their is not guarantee that the Constitution will work as intended, there is no guarantee that a fair-minded reader trying his best will correctly understand even the most important points.
Thus, the need to rely on external authorities becomes important when dealing with the Constitution in ways that it is not when dealing with the Bible.
Like the Fathers, the Founders were not always of one mind. In one interaction I had with a Roman Catholic, I recall the following interchange (I'm paraphrasing):
RC: Are you saying that church went off the rails from the very beginning? Because we know what Clement of Rome taught about ecclesiology.
TF: You're referring to the book of 1 Clement, which is usually attributed to Clement of Rome. But note that the author of that work was arguing with the Corinthians. He was saying that they went off the rails. So, did someone go off the rails right at the beginning? Apparently so - the very evidence you cite is proof of that, whether Clement was right or wrong.
A similar issue was recently raised by my brother, Jordan Hall, in a post about the Constitution. There he raised a comment by Thomas Jefferson in a letter written around 1819. My brother wanted to argue that Jefferson's position reflected what "the Founders" thought about the Constitution. The problem is this - Jefferson's letter is one that is arguing against his contemporaries (link to letter). In other words, while my brother may want to side with Jefferson, Jefferson is arguing with another of his contemporaries. "The Founders" were not of one mind on the subject, but of two (or more) competing minds.
That leads us to another similarity. It's not always easy to identify a "Founder" just as it is sometimes difficult to identify a "Father." Should we count Origen and Tertullian as Fathers? They are certainly highly influential early Christian authors, but their full orthodoxy is sometimes questioned. Similarly, who do we count as a Founder? One Constitution-focused website explains the problem:
Other U.S. Founding Fathers were not there [TF insertion: at the Constitutional Convention], but made significant contributions in other ways. Thomas Jefferson, who wrote the Declaration of Independence, was serving as ambassador to France at the time of the Convention. He kept abreast of the proceedings in Philadelphia by carrying on correspondence with James Madison. John Adams, as ambassador to Great Britain, wrote "Defense of the Constitution of the Government of the United States of America." Thomas Paine wrote the influential pamphlet "Common Sense," which immeasurably influenced the philosophy reflected in the Declaration of Independence. One of the U.S. Founding Fathers, Patrick Henry, was initially opposed to the very idea of the Constitution! He wanted to keep the Articles of Confederation, the predecessor to the Constitution. However, when an agreement was made to add a "bill of rights" to the Constitution, Henry fought hard for its ratification.(link to site)
We see similar divisions amongst the fathers. There were various theological battles over which those in the early church fought - sometimes on central issues (like Jesus' divinity) and sometimes over relatively trivial issues (like when Easter should be celebrated). While I certainly wouldn't treat an Arian as a "father of the church," it's important to realize that this identification involves me using the Scripture as my standard for deciding who to label a "father." Thus, my list of "fathers" is going to include generally orthodox men. I can't then turn around and say that their opinion proves that my doctrine is orthodox, as Roman Catholics sometimes erroneously attempt to do.
People who are trying to round up opinions of the Founders to support their views need to be similarly careful. Jefferson's view on the judiciary (as interpreted by my brother) would seem to place him at odds with John Marshall's views on the judiciary. Nevertheless John Marshall, like Thomas Jefferson, was a founding father (link to relevant information on Marshall). Although Jefferson is more famous, both men were founders and arguably represent (on some issues) competing views found amongst the Founders even in the early days of the republic. If you only count the Founders who agree with you as being Founders, your appeal to them is no longer grammatical-historical analysis but simply partisan politics or propaganda.
So be careful when applying external sources. The Constitution may need them to be understood-- Scripture doesn't need them, even if they are helpful. Moreover, when you are looking at them, look more for the points on which those debating found common ground. In the case of the Fathers, that was that Scripture is the highest and most ultimate authority, aka Sola Scriptura. Look for the things that they took for granted that their opponents would agree with, not those points on which they wanted their opponents to submit. Those points provide much stronger evidence for "the opinion" of the Fathers or the Founders.