What does “for Mr. Spicer, The Mooch was a bridge too far” mean?

Solution 1:

The term a bridge too far is a bit like the final straw (...that breaks the camel's back).

It derives from the film A Bridge Too Far (1977), which was a dramatisation of the British airborne attempt to hold the Rhine bridge at Arnhem in September 1944. Other bridges en route to Arnhem, at Eindhoven and Nijmegen, were successfully held intact for the main column to cross. Despite seizing the town of Arnhem behind enemy lines and holding the bridge for three days, the Paras are eventually overcome by German tanks, with the main attack unable to relieve them. One of the British commanders is attributed as having said something like we have gone for a bridge too far.

Solution 2:

It is probably worth noting that mooch is a very old term with different meanings. This is not to say that any of these meanings lies at the origin of Mr. Scaramucci nickname, which is most likely due to the assonance with the last part of his surname "mucci".

Mooch:

• It’s actually a most interesting word, one which has been around on the margins of the language since the fifteenth century with a set of meanings, none of them pleasant.

• In its earliest days, to mooch meant to pretend poverty or act the miser. That may come from an even earlier word, mitch, which by then had been in existence for a couple of centuries with a similar meaning. The latter is believed to derive from the Old French muchier or mucier, which meant to hide, or more pejoratively, to skulk or lurk. Both mitch and mooch survived in several senses in local dialects in Britain for centuries, with the latter becoming by far the better known.

• Mooch could variously mean to play truant (in particular to pick blackberries, for some unknown reason), to “loaf, skulk, sneak, or loiter” as the OED puts it, or to steal or pilfer. In the 1850s, it look on the sense you mention — to sponge on others, to borrow money or cadge things, or to slip away and let others pay for your entertainment. This is clearly where the modern American sense that you quote comes from.

• But it has had other senses in North America, among them to troll for fish, especially on the West Coast. In the 1920s, it was a slang term among gamblers or on fairgrounds for a sucker or easy mark. In the 1940s-50s, the noun could also refer to a drug addict, so to be on the mooch was to be addicted and a mooch pusher was a drug dealer.

(World Wide Words)