The shooting happened on March 30, 1981 at 2:27 PM; the would-be assassin, John Hinckley Jr., tried to kill Reagan thinking it would get him the attention of actress Jodie Foster. In addition to hitting Reagan, three others were injured, including the press secretary James Brady.

At this time Vice President Bush was on Air Force Two, flying to Texas. Haig tried to call midflight

George, this is Al Haig! Turn around! Turn around!

although the connection was fuzzy.

A group including Chief of Staff Baker and Deputy Press Secretary Speakes went to the hospital, at the time still thinking (as a news story that Bush was watching on Air Force Two said) the president was not hurt.

Eventually, the word got back to the White House that Reagan was in fact seriously injured (he came close to dying) and Haig, stymied by the voice call, had gotten through with a coded cable.

Mr. Vice President: In the incident you will have heard about by now, the president was struck in the back and is in serious condition. Medical authorities are now deciding whether or not to operate. Recommend you return to D.C. at the earliest possible moment.

(The plane continued to Texas before Bush flew back -- it needed refueling before it could go back to D.C., but the pilot rushed back as fast as he could.)

In the meantime, Deputy Press Secretary Speakes had arrived directly back from the hospital to the press room around 4 pm, not visiting the Situation Room first. Things started to go badly; he was clearly frazzled and nervous. He was definitely lacking in information, not able to answer if the Vice Present was going to assume emergency powers, and who would assess that. (Normally it would be the more experienced James Brady answering questions, but remember he was one of the ones injured -- in fact he was hurt the worst of all, suffering a head wound and permanent brain damage.)

Haig, watching from the Situation Room, and concerned about appearance to the allies of the US (and enemies -- the possibility of the USSR exploiting the situation was raised) said "Speakes should not be answering questions" and "we've got to straighten this out."

Haig came down to the press room in an attempt to clarify, but generally made things worse, and infamously had this exchange:

Bill Plante, CBS: Who's making the decisions for the government right now? Who's making the decisions?

Haig: Constitutionally, gentlemen, you have the president, the vice president, and the secretary of state in that order and should the president decide he wants to transfer the helm to the vice president, he will do so. As of now, I am in control here, in the White House, pending return of the vice president and in close touch with him. If something came up, I would check with him, of course.

Speakes later described Haig as being panicked under pressure, that

...the beads of perspiration on his forehead and his out-of-breath declaration gave a concerned public reason to worry. From then on, other members of the Reagan team would be viewing him with suspicion...

It does appear that Haig was simply confused here, and was trying to convey "in terms of running the administrative White House activities in response to this crisis" and not "I have the literal constitutional powers". His own explanation later:

I was wholly intent on correcting an impression of confusion and indecision that Speakes's words may have inadvertently created... My remark that I was 'in control .... pending the return of the Vice President' was a statement of the fact that I was the senior Cabinet officer present. I was talking about the arrangements we had made in the situation room for the three- or four-hour period in which we awaited the return of the Vice President from Texas. Less precise, though in the same context, was my statement that 'constitutionally ... you have the President, the Vice President, and the Secretary of State, in that order.' I ought to have said 'traditionally' or 'administratively' instead of 'constitutionally.'

Two others from the White House noted:

I personally had discussions with Haig in which we agreed that he would be our point of contact here in the situation room of the White House, as he quite properly should have been as the senior Cabinet officer...

and

...it was understood that Haig, as the senior Cabinet officer, should run the Situation Room.

A third comment, from an interview with John Kelly of the Department of State:

It was an unfortunate phrase because all he wanted to convey that he was the senior Cabinet officer present; there is no doubt in my mind that he was not trying to usurp the prerogatives of various officials, but his comment contributed to Haig’s reputation as a “hot head.”

Some additional evidence of this is simply that Haig was the one quite emphatically and desperately trying to get Bush back to D.C. Everyone understood that Bush would be in charge as soon as he arrived, which he did so at about 7 pm, sitting at the head of the table, greeting Haig as he came in:

Hi, Al, how are you? Good to see you.

There was no reference at all to Haig's earlier statement.

...

Abrams, H. L. (1994). The President Has Been Shot: Confusion, Disability, and the 25th Amendment. United States: Stanford University Press.

Peppard, A. (13 May 2015). Command and Control: Tested Under Fire. The Dallas Morning News.

Wilber, D. Q. (2011). Rawhide Down: The Near Assassination of Ronald Reagan. United States: Henry Holt and Company.