Almost immediately the American media jumped all over Carson, because at the time the Constitution was being drafted, Jefferson was serving in France as a U.S. minister. The political left was even more vicious in their attacks.
But, here's the thing. Jefferson didn't have to be in this country to have provided input into the crafting of the Constitution. He simply corresponded with those drafting it. For example, the Library of Congress makes this comment about a letter sent to Madison in 1787 after reading a draft of the Constitution:
"Thomas Jefferson's December 20, 1787, letter to James Madison contains objections to key parts of the new Federal Constitution. Primarily, Jefferson noted the absence of a bill of rights and the failure to provide for rotation in office or term limits, particularly for the chief executive. During the writing and ratification of the constitution, in an effort to influence the formation of the new governmental structure, Jefferson wrote many similar letters to friends and political acquaintances in America."We know, today, that a Bill of Rights was added as the first ten amendments which defined personal freedoms and limited the scope of government. So, Jefferson's input was influential. The only mistake that Carson made was in saying Jefferson "tried to craft" which implies that he was the actual author of the Constitution.
Carson flubs Thomas Jefferson's role in the Constitution: http://www.cnn.com/2015/11/23/politics/ben-carson-thomas-jefferson-constitution-founding-fathers/
Ben Carson Doesn't Know Who Wrote The Constitution: http://www.forwardprogressives.com/ben-carson-constitution/
Library of Congress: Thomas Jefferson: http://www.loc.gov/exhibits/jefferson/jefffed.html
United States Bill of Rights: https://en.wikipedia.org/wiki/United_States_Bill_of_Rights