http://rs6.loc.gov/cgi-bin/query/r?ammem/hlaw:@field%28DOCID+@lit%28fr003452%29%29
link to the index citing Vattel.
First page search for Vattel..
Items 1 through 20 of 44
1 Letters of Delegates to Congress: Volume: 3 January 1, 1776 - May 15, 1776 —Benjamin Franklin to James Bowdoin
2 Elliot’s Debates —Wednesday, June 27.
3 Farrand’s Records —MADISON Wednesday June 27. in Convention
4 Letters of Delegates to Congress: Volume 22 November 1, 1784 - November 6, 1785 —Elbridge Gerry to Timothy Pickering
5 Letters of Delegates to Congress: Volume 8 September 19, 1777 - January 31, 1778 —Daniel Roberdeau to Timothy Matlack
6 Letters of Delegates to Congress: Volume 8 September 19, 1777 - January 31, 1778 —Elbridge Gerry to Thomas Wharton
7 Farrand’s Records —KING Wednesday 27. June5
8 Farrand’s Records —YATES Wednesday, June 27th, 1787.
9 Elliot’s Debates —Wednesday, June 27, 1787.
10 Letters of Delegates to Congress: Volume 2 September 1775 - December 1775 —Richard Smith’s Diary
11 Letters of Delegates to Congress: Volume 8 September 19, 1777 - January 31, 1778 —James Lovell to John Adams
12 The Revolutionary Diplomatic Correspondence —Franklin to Dumas.*
13 Senate Journal —MONDAY, MARCH 10, 1794.
14 Letters of Delegates to Congress: Volume 2 September 1775 - December 1775 —Charles William Frederic Dumas
15 Journals of the Continental Congress —FRIDAY, NOVEMBER 25, 1785.
16 Letters of Delegates to Congress: Volume 16 September 1, 1780 - February 28, 1781 —James Madison to Joseph Jones
17 The Revolutionary Diplomatic Correspondence —Franklin to R. Bernstorf, Minister of Foreign Affairs in Denmark.*
18 The Revolutionary Diplomatic Correspondence —Dana to Livingston.*
19 The Revolutionary Diplomatic Correspondence —A. Lee to the King of Prussia.
20 Congressional Globe —INDEX TO THE APPENDIX.
None have a direct notation for the Natural Born requirement. However, they all put to bed the lie that the Founders did not use - extensively - the precepts that Vattel stipulated in his The Law of Nations.
This list apparently contains references to de Vattel
http://memory.loc.gov/cgi-bin/query
Example:
Letters of Delegates to Congress: Volume 8 September 19, 1777 - January 31, 1778
Elbridge Gerry to Thomas Wharton
Dear Sir York in Pennsylvania Novr 8. 1777 The following Books are much wanted by some Gentlemen of Congress, & are not to be procured in this Place; if they are to be found in the Pennsylvania Library, which We are informed is removed by Order of your Excellency to Lancaster, I shall be much obliged to You for the Loan thereof being with respect your Excellency’s very huml sert,(1) E Gerry
Vattell’s Law of Nations
Grotius
Puffendorf (2)
RC (PHi). Addressed: “His Excellency Thomas Wharton Esqr. Lancaster.”
1 In his November 11 response Wharton informed Gerry that “the Library you Speak of was not removed, it still remains in the City for the edification of Tories.”
Wharton added that there was a library in Lancaster that might be willing to lend books to members of Congress. Gerry Papers, DLC.
Before Wharton responded, Daniel Roberdeau sent a request for the same works to Wharton on November 10. “A Committee of Congress have occasion of the under mentioned Law Books,” Roberdeau explained, “which one of them sais were in the Library belonging to the State in Philada. Therefore I am desired to apply to you for the immediate Loan of them, and that they may be sent by express, if a good Opportunity does not very soon offer. If the books of the State were not brought to Lancaster you are requested to borrow these books of some Gentleman there and forward them.” Continental Congress Miscellany, DLC; and Pa. Archives, 1st ser. 5:757.
2 Emmerich de Vattel, The Law of Nations or Principles of the Law of Nature Applied to the Conduct and Affairs of Nations and Sovereignty; Hugo Grotius, On the Law of War and Peace; and Samuel Pufendorf, of the Law of Nature and Nations.
Page 243
NOVEMBER 8, 1777
But this should at least put to rest the notion that Vattel was just some obscure Swiss philosopher.