What does “Has it come to this?” in “Republican leaders quickly voiced horror at these tactics. ‘Has it come to this?’ said John Boehner” mean?

John is expressing his horror at the tactics by "asking" the somewhat rhetorical question "Has it come to this?". This phrase implies that he almost cannot believe that such tactics would be used, hence voicing his horror, as mentioned.

In this phrase, it is hard for me to think of what "it" represents, but I could say that it could mean "their desperation" -

"Has their desperation come to this?"
"Has their desperation really increased this much?"
"Have they really become this desperate?"
"Have they really become so desperate that they would use such tactics?"

In "Has it come to this?", the word it is a dummy pronoun. It stands for "the state of things as they are".

As another answer notes, John Boehner's remarks are rhetorical, intended to make it appear as if the Democrat methods are completely immoral as opposed to politics as usual. (Of course they may be both.) Note, the phrase "holding the economy hostage" is often heard when the US federal budget is overdue; in the case at hand, it might refer instead to the uncertainty that afflicts American business when tax law is in flux, which makes tax-planning like gambling.

Your suggestion ("How it come to this?") is ungrammatical; however, one can say "How has it come to this?" or "How did it come to this?".

More often than not, "Has it come to this?" is used to convey intense concern and possible disgust and disappointment at the current situation (pertaining to the topic of discussion), without having to articulate what exactly about the situation demands such a concern. In other words, the phrase is employed for dramatic effect by leaving what "come" and "this" refer to, to the imagination of the reader, because writing it out in words would not have the intended effect.

Obligatory XKCD:

_{Comic #1022}

'Has' is correct. The pattern:

Has it come to this?

is general surprise that events have unfolded in this manner. One is seeing an unwanted event and wondering how things have changed from before that would lead to such a thing.

For example:

Children talking back to their parents? In my day, any child would be scared to death to speak with such impertinence. Nowadays, they'll tell you to shut up and get out of the way of the video game as much as brush a fly away. To get them to listen to you, you have to mention money. Has it come to this?

One might also say "How has it come to this?" (in what way have things arrived at this situation).

The "it" is non-referential. It's not the totally empty 'there' in 'there is', but is somewhat general, meaning 'things' or 'All relevant events so far'.

I think the intent here is has the tax cut situation come to this fork in the road. The Republicans either have to raise taxes for the wealthy or the Democrats will let the tax cuts expire causing the taxes to increase either way. So it's basically saying that the Democrats have given the Republicans an ultimatum to pick which route they want to go, raise taxes themselves or let the tax cuts expire causing the same outcome. The statement really speaks to the dirty hand that the Democrats are playing in that they have to either do it or the Democrats will force it to happen.