Not sure if this has been posted yet but here is the definition of "Blue Dog"

The pic is of the dog from that hrc tweet.

Blue Dog

noun [ C ] POLITICS specialized (also blue dog)

UK/ˈblu ˌdɒɡ/ US/ˈblu ˌdɑːɡ/

in the US, a politician or voter who supports the Democratic party but is on the conservative side of the party:

She is a conservative Blue Dog Democrat who cannot be counted on to vote the party line.

He was an Iraq war veteran and a member of the Blue Dog Coalition, a group of self-identified Democratic moderates and conservatives.

These tax measures caused problems with the blue dogs on Capitol Hill.

https://dictionary.cambridge.org/dictionary/english/blue-dog