Do you understand "New Deal" to mean a new bargain or a new hand of cards?

I researched the expression a little and found that an advisor to FDR in 1933 had picked up the phrase, used by Mark Twain* in A Connecticut Yankee in King Arthur’s Court (1889). It appears in a chapter called “Freemen,” which has an extraordinary satirical resonance with what we are seeing right now.

In Dictionary.com I found a mention that the expression was a political slogan of Andrew Jackson’s in 1830–1835, well before Mark Twain used it, but I couldn’t corroborate that elsewhere.

What I don’t find is a restatement of the literal or metaphorical sense of the expression.

I always thought the expression meant a new bargain or agreement; but now I’m wondering if it means being dealt a fresh hand, as in a card game.

How do you understand it?
 

*Part of the pertinent passage follows, describing a (fictional) medieval political system; the whole chapter is wonderfully ironic in light of today’s political climate.

And now here I was, in a country where a right to say how the country should be governed was restricted to six persons in each thousand of its population. For the nine hundred and ninety-four to express dissatisfaction with the regnant system and propose to change it, would have made the whole six shudder as one man, it would have been so disloyal, so dishonorable, such putrid black treason. So to speak, I was become a stockholder in a corporation where nine hundred and ninety-four of the members furnished all the money and did all the work, and the other six elected themselves a permanent board of direction and took all the dividends. It seemed to me that what the nine hundred and ninety-four dupes needed was a new deal.