Proper term for a "Swipe"

Question

You see it a lot from politicians. For example:

“I understand the House Republican leadership is in disarray, but they shouldn’t wait two weeks before holding a vote. Our troops should be a priority and I urge the House to hold a vote as soon as possible so we can get back to crafting a more responsible solution.”

What would the first part of this sentence be called? I believe the media would refer to this as a "swipe" but is there a more formal term? A couple of points I think should be considered:

1. They are not trying to be directly insulting by tying the "swipe" to a message
2. However, the "swipe" really has nothing to do with the message (they should vote sooner)
3. The "swipe" is never flattering but its also usually not something that extremely incendiary either.

Thanks in advance.

Answer 1

A barbed remark or joke seems polite or humorous, but contains a cleverly hidden criticism.

Example: The visiting British Foreign Secretary, Philip Hammond, and Israeli Prime Minister, Benjamin Netanyahu, exchanged a series of barbed remarks in a meeting that underscored the sharp differences between Israel and world powers over the nuclear agreement with Iran.

Answer 2

One term is "potshot," meaning "a critical remark made in a random or sporadic manner."

Example:

to take a potshot at military spending in a speech on taxation

Answer 3

There's nothing wrong with swipe.

E.g., "His message [took/made] a [swipe/ jab/ punch/ quip/ gibe/ cheap shot] at our group." Read on, below the page break, to see what they were doing, in the answer I wrote while I thought you were concerned with the second sentence's guilt trip, as opposed to the first one's insult.

However, taken as a whole, the entire thing is an insult. One that says that, "because ya'll can't get your act together, people are dying."

My favorite for this cunning use of language is quip:

a clever usually taunting remark –MW

Note as of this post, this is the third answer presenting a word that modifies, or contains in its definition, the word remark. Mayhaps you should do a reverse lookup on it.

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Funny that you should mention politicians; it's in their job description:

politics pol·i·tics /ˈpäləˌtiks/ noun

activities within an organization that are aimed at improving someone's status or position and are typically considered to be devious or divisive. –Google

The idiom is: playing politics.

to allow politics to dominate in matters where principle should prevail. –TFD

There may well be a fancier word for this type of guilt trip, but it always boils down to politics.