Dumbest sign I've seen at the Tea Parties?
No, he wouldn't. Who are we talking about "overthrowing"? The government? Jefferson resigned as Secretary of State in the Federalist administration of Washington, but didn't call for the overthrow of the government. He served as Vice-President under a Federalist president (John Adams) and didn't call for the overthrow of the government. Jefferson may have thought that, even in a society with free elections, things could get bad enough that the government should be changed, but that was always the action of last resort. Don't put the cart before the horse.
All of the Jefferson fans so inordinately fond of quoting his "Tree of liberty/blood of tyrants" line really should realize that it's only one man's opinion (and a minority one at that), not American Gospel.