Neology

Sounds like the opposite of "stop on a dime" to me.

Yeah, I think a couple of sites that talked about the phrase said it had something to do with a dancing couple stopping somehow literally "on a dime" and then being told to move off of it.

But I think that only works if you think of being on a dime as standing in one place without moving much or far. 'Cause to me, the phrase "stop on a dime" implies coming to a stop in a very short space, rather than staying still in that small space after you've stopped.

To put it another way: If "get off the dime" meant "get moving after a sudden stop," that would make sense to me as an opposite of "stop on a dime"; but instead it seems to mean "get moving after a prolonged period of non-moving," which doesn't (to me) fit so well with "stop on a dime."

For whatever it's worth:

It should be noted that, in this instance, answers.com gets its information from The American Heritage Dictionary of Idioms (1997).

The oldest example of this in the New York Times is from February 1943, quoting a labor leader on a strike by Boeing employees:

Earlier he had said that the "WLB had been lulled to complacency through lack of physical demonstration by aircraft workers" and added:

"We are fed up. We are going to tell the WPB to get off the dime."

The next NYT citation's from 1954, again with regard to a labor dispute:

Mrs. Rosenberg said the committee was trying to determine what could be done "to get off the dime."

American Slang (a 1987 abridgement of the New Dictionary of American Slang) has:

get off the dime v phr To start; stop wasting time: How do we get off the dime we're on? —New York Times

get off the dime (informal) be decisive and show initiative: at some point you have to get off the dime and do something.

2001 U.S. News & World Report Congress must get off the dime and redeem the commitments that President Bush made to New York City.

(Man, I wish I still had access to UMich's databases. And I'm gonna lose access to Emerson's shortly. Somebody needs to form a consortium for non-academics who want to sign up for lots of reference works as a package deal.)

I've heard and used myself the term "get off the dime" and when I did I meant "Move, stop being paralyzed, unable or unwilling to decide to act".
As a child in the 60s/70s I lived surrounded by older folks (in their 60s 70s/80). One site says "This expression originated in the 1920s in dance-halls as an imperative for dancers to get moving. By 1926 it had been extended to other activities. " Remember "dime a dance"? Perhaps it meant stop dancing with one dance partner and move on to another?
All I can confirm is that I heard this expression (since the 60s) used to mean exactly what it is said to mean.

I think it might refer to a "paradigm shift." This is a usage I found on the web.

http://www.dvorak.org/blog/?p=4719

Kent, while I agree about the need for diversity, it was, after all, discovering the ability to propagate cereal crops that moved us off the dime — from hunter/gatherers to primitive agriculture. Over those thousands of years, there have been numerous predominant cereal grains [my personal favorite still being farro]. There is tremendous diversity within what is done with those grains — whether it’s tofu or cattle feed, bread or beer.

Four is doing pretty good.