I'm seeking a quotation from an early American president -- I believe
it was Jefferson's, but I'm not sure.  It has something to do with
criticism: in it, the writer confesses that the effect of even mild
censure outweighs the positive effect of much high praise.
     The passage may have appeared in a personal letter from the one
who wrote it (Jefferson?) to another president.  But I am not sure of
that.

Hi john_bullock, 

You are correct in believing this quote is by Thomas Jefferson. The
actual quote is:

“I find the pain of a little censure, even when it is unfounded, is
more acute than the pleasure of much praise.”
 
ATTRIBUTION: Thomas Jefferson (1743–1826), U.S. president. Letter,
March 13, 1789.

Source: Bartleby: The Columbia World of Quotations
http://www.bartleby.com/66/44/30744.html


This quotation was indeed in a letter from Thomas Jefferson written to
Francis Hopkinson.
Below is the excerpt of the letter which contains the quote:

“My great wish is to go on in a strict but silent performance of my
duty; to avoid attracting notice & to keep my name out of newspapers,
because I find the pain of a little censure, even when it is
unfounded, is more acute than the pleasure of much praise. The
attaching circumstance of my present office is that I can do it's
duties unseen by those for whom they are done.”

You can read the entire letter here:

MIT Lab: The Letters of Thomas Jefferson
http://www.ai.mit.edu/people/hqm/writings/jefferson/odur.let.rug.nl/usa/P/tj3/writings/brf/jefl75.htm


The following are other sites where this quote is found:  

Entplaza: Quotations on Censure
http://www.entplaza.com/cgi-bin/create/quotes.pl?cat=Censure

The Other Pages: Quotations
http://www.theotherpages.org/topic-c1.html

MemorableQuotations.com
http://www.memorablequotations.com/jefferson.htm

University of Virginia Library
http://etext.lib.virginia.edu/etcbin/foley-page?id=JCE1161

IFLA: Quotes by origin
http://www.ifla.org/faife/litter/origin/j.htm


Search criteria:
quotes American president criticism praise
quote jefferson criticism  praise
“pleasure of much praise”

I hope this is helpful. If you have any questions regarding my answer
please don't hesitate to ask before rating it.

Best regards,
rainbow-ga

This is an outstanding answer, markedly more detailed than I expected.

Hi john_bullock,

Thank you for your comment, rating and tip!

Best regards,
rainbow~