I *think * its’ from Twelfth Night. Our hero (I’m certain its’ a guy) has a monologue in which he scolds himself for not talking to a girl he likes. Something like: What devils cause my tongue to cleave to my palate? My Google skillz are failing me. Little help?
ORLANDO. What passion hangs these weights upon my tongue?
I cannot speak to her, yet she urg’d conference.
O poor Orlando, thou art overthrown!
Or Charles or something weaker masters thee.
from As You Like It
That’s all I’ve got.
Doesn’t sound familiar. But that last line is nicely iambic. 
As You Like It, A1S2:
ORLANDO
What passion hangs these weights upon my tongue?
I cannot speak to her, yet she urged conference.
yea or nay? Are you sure on the devil/cleft thing?
(The beauty of Shakespearean quotes, of course, is that it’s all public domain, so full texts are readily available for the searching).
The rottenness being that others on the board search for the same quotes just as quickly, and win a simulpost. Darn you, ddgryphon! Darn you to heck!
The only similar quote I could find, and the context is different from what you describe, came from Richard II.
Yes! Wow, was I off. I thought the guy’s name was Orlando, but I wasn’t sure. Thanks!