Learn English – Grammatical construction of “to have happen”

To answer the original question, it's Present tense, and the verb construction is Perfect. Together they're often called "Present Perfect", which is a tense in Latin. but only a construction in English.

Yes, have got is an idiom; but that explains nothing except its irregularity, of course. And it's a different idiom in UK English than it is in American English, where it contrasts with have gotten. Like most idioms, where it came from is a long tortuous story.

Get means come to be or come to have, as in

• He got tired. ~ He became tired.

or

• He got his orders. ~ He received his orders.

(I've always been bemused that in German the verb bekommen means receive but not become.)

In the case of have, especially, if one comments on the acquisition of something, the implicature is that one still has it -- otherwise, one would say something different. So the present perfect of get naturally implicates the present of "have", leading to the equivalence of have got and have.

The Present Perfect construction uses the auxiliary verb have/has, plus the past participle of the matrix verb:

• I have/He has gone.

The past participle of get is got or gotten in the US; UK mileage may vary. There is a principled distinction between the two, since get -- as the inchoative form of both be and have -- is itself an auxiliary, and got has come to have its own usages in American English, leaving the simple Past Participle slot to be filled by gotten.

As McCawley points out, one of the functions of the Perfect is to report past actions still relevant in the present; thus,

• I've got a cold

reports a past event (catching the cold) which is still relevant (having the cold), and, since pragmatically what we're interested in is the present state, I've got a cold is used more often to warn people to duck when I sneeze than to comment on the events of the past week.

But wait – there's more. Both be and have are already auxiliary verbs, and are used in many constructions, like Passive or Perfect. Since get can implicate be and have in some cases, it's been generalized to substitute in others, where their use is grammatical instead of meaningful, like the so-called Get-Passive

• He got arrested. ~ He was arrested. = s.b. arrested him.

or in the periphrastic modal have to meaning must

• He's got to go. ~ He has to go. = He must go.

(frequently spelled gotta, because the /v/ or /z/ in /ðevgaɾə/ /hizgaɾə/ is usually inaudible)

or simply, wherever one might use have

• I got a new DVD. ~ I have a new DVD.

Quite frequently children generalize this equivalence to produce sentences like

• He gots a new ball.

in effect, inventing a new verb because the old one has worn out.

Got all that?

This is a very rare usage and cannot be regarded as idiomatic today.

Dare is an odd word—it wanders back and forth between performing as an ordinary lexical verb and as a sort of modal. For instance, it is used with both marked and unmarked infinitives, and it may be used with or without DO-support:

I dare tell you so. ... I dare to tell you so.
I dare not tell you so. ... I do not dare tell you so.
Dare I eat a peach? ... Do I dare to eat a peach?

I dare have spoken/told is a use consistent with treatment as a full modal—except that every instance of such use I find (in a quick-and-dirty survey on Google Books) employs the present form in a past sense, as your example does. This suggests that the few authors who used it (all such uses I found appeared in the last half of the 19th century) were influenced—and somehow confused!—by the conventional of use of the “perfect infinitive” to backshift past modals employed in a present sense, as when “I might do this” is backshifted as “I might have done this”.

It’s a fascinating phenomenon, and I am glad to have had it drawn to my attention. But it was never common, and for practical purposes you may ignore it.