Here is a copy of Bob Woodward's 1977 article breaking the story in the Washington Post. However, I don't see much information on how the people and political classes of Jordan reacted to finding out their head of state was a paid foreign agent.
This is very much a case of dueling historians. The two major scholarly biographies of King Hussein (by Nigel Ashton and Avi Shlaim), take, shall we say, very different approaches to this incident.
Ashton calls the Woodward story "sensationalized and inaccurate". The payments that started in 1957 were 5000 dinars a month and destined for individuals in the army and intelligence service, and stayed that way all the way up to the 1973-1974 when some children of the royal family attended school in the US; the extra money was for the security detail. Ashton indicates the story caused trouble in King Hussein's dealing with his enemies (who called him a crypto-Zionist).
Shlaim includes a CIA source that mentions the story mostly as Ashton tells it, but includes a more sinister take with a source mentioning payments in the "form of Jordanian dinars delivered in a plain envelope" and that
Ready cash was what the king needed and what the CIA provided. The acronym CIA stood for the Central Intelligence Agency, but in this case, as in so many others, it could equally have stood for Cash In Advance.
So for what follows, I'm interpolating the best I can:
Reaction #1: Believe that it's just a Zionist conspiracy.
The Woodward story came out Februrary 18th; in the February 19th issue of the Jordan Times there was this:
The article in question ... contains fabricated and incorrect information meant to defame Jordan and its leaders ... This is evident from the timing of the publication of the article -- on the event of the U.S. secretary of state's vist to Jordan. The Washington Post and the author of the article are known for their close affiliation with Zionist organizations in the United States.
No doubt -- then as now -- some people simply believed the official line as printed.
Reaction #2: Surprise that the article was printed, but not at the corruption.
Even Ashton's charitable depiction of events gives the impression that the money flowing from the CIA flowed to many hands; an interview from Shlaim of a senior civil servant (Mreiwad al-Tall) notes
Part of the agreement with the Americans was that Hussein would allow the CIA to recruit any Jordanian to work for them. The CIA gave the king personally $3 million a year. The CIA station chief in Amman used to come with a briefcase to the palace once a month and hand the money to Hussein.
The briefcase story is dubious; it contradicts all the other sources (even the negative ones) but it does give a snapshot of the general reaction: the country was awash in money from the CIA.
Reaction #3: Both believing that the corruption existed and surprise at the corruption.
Shlaim indicates people of this category existed, but does not produce examples of any.
The various sources imply, among the political classes, that Reaction #2 was the common reaction (either you were one of the ones taking bribes, or you were upset about it). The sources are silent about the general public.
There was a follow-up asking about Jordan's equivalent to the CIA, the Jordanian General Intelligence Directorate (GID). They are well-known for having joint operations with the CIA and have often received CIA money. The US began training Jordanian officers in the mid-1970s. George Tenet (former director of the CIA) outright told Bob Woodward: "We built the GID."
You might say, that: yes, they already knew.
Sources:
Ashton, N. (2008). King Hussein of Jordan: A Political Life. Ukraine: Yale University Press.
Loeb, V., O'Connell, J. (2011). King's Counsel: A Memoir of War, Espionage, and Diplomacy in the Middle East. United States: W. W. Norton.
Moore, Pete. (2017, August 1) Jordan's Long War Economy. Jadaliyya.
Shlaim, A. (2009). Lion of Jordan: The Life of King Hussein in War and Peace. United States: Vintage Books.
Woodward, B. (1999). Shadow: Five Presidents And The Legacy Of Watergate. (n.p.): Simon & Schuster.
Follow-up question: Did Jordan have its own intelligence agency at the time? Was it independent or did it support any of the "big names" in intelligence at the time (Mossad, CIA, KGB, MI6, SDECE, etc.)? How did they react to those news?