What does ‘Break out the corsages’ mean?

From Wikipedia:

Corsage refers to a bouquet of flowers worn on a woman's dress or worn around her wrist.

A corsage is an item typically worn at a prom or similar event.

The use of this expression is because of the topic of legislators having to pick partners, which can draw a humorous comparison to a prom. The State of the Union address had traditionally been a time of strong partisanship. The idea to pick partners from "across the aisle" is an attempt to show the supposed bipartisanship of the current legislature.

An article explaining the details of this plan is available here. Quoting from the article:

In a letter to his fellow lawmakers, Udall said the partisan seating arrangement has become a negative symbol of the divisions in Congress - and among the American people - with one side of the chamber cheering and applauding loudly throughout the President's speech, while the other often sits silent. He urged them to bridge the partisan divide by sitting together as a symbolic gesture signifying unity and better reflecting the communities they represent.

The term "break out" is often used colloquially for "getting out" or "taking out" something. For example, "Let's break out the champagne" could be used to express the appropriateness of celebrating some event (although this particular term is often used sarcastically). A search on Google reveals some interesting use of this syntax.

YourDictionary.com has a definition as well:

1. Develop suddenly and forcefully. For example, A fire broke out last night, or He broke out in a sweat. [a.d. 1000] 2. Be affected with a skin eruption, such as a rash or boils, as in A teenager's face often breaks out in pimples. [c. 1300] 3. Prepare something for consumption, action, or use, as in Let's break out the champagne, or It's such a fine day—let's break out the fishing rods. [Early 1800s] 4. break out of. Force out by breaking; also, escape from confinement. For example, The hurricane broke the glass out of all the windows, or He broke out of prison but was soon apprehended. [Early 1600s] 5. Isolate a portion of a body of data, as in Please break out the sales figures from the quarterly report. [Mid-1900s]

"Break out" in this context refers to getting out of storage something long kept, as in 'Break out the champagne, I'm getting married!". So if a prom (or other dance) was announced, the girls might break out their best dresses and corsages. The Washington Post thinks this is a suitably humorous comparison for the Senate.

Since a corsage is an article of extremely formal women's clothing, I suppose that combines the idea of forward-looking preparation (they're making plans, but not yet getting dressed for the occasion since it's still some time in the future), combined with an insult to the masculinity of the predominantly-male congress. The latter aspect could have been avoided by using a word such as "tuxedo" instead.