Matching verbs to collective nouns
Collective nouns are nouns which stand for a group or collection of
people or things. They include words such as audience, committee,
police, crew, family, government, group, and team.
Most collective nouns can be treated as singular or plural, with
either a singular or plural verb:
√ The whole family was at the table. [singular verb]
√ The whole family were at the table. [plural verb]
There are a few collective nouns which are always used with a plural
verb, the commonest of which are police and people:
√ She’s happy with the way the police have handled the case.
X She’s happy with the way the police has handled the case.
If you aren’t sure whether to use a singular or a plural verb with a
collective noun, look it up. Most dictionaries will tell you which is
correct.
Source: Oxford Dictionaries
People is the plural form of person e.g."A person lives in that apartment" [singular verb] and "Several people live in that building" [plural verb]
Hence the beginning of the OP's sentence should read:
The people of the US have...
(note the addition of the definite article, which must precede either US or USA).
Alternatively, one could use the singular collective noun population instead of people:
The population in the USA has approximately doubled over the past 50 years, with a total
population of 302 million (as at July 2007):
Source
A people
When speaking about a class, a nation, a community or any specific population then the expression a people can be used, in that case a people is a singular noun because it represents everybody in that particular group, it is an entity, a total sum, a single unit. I might even describe it as a type of mass (or uncountable) noun; however, it is not grammatical to say: A people of the US is, instead we say:
The US is a patriotic people
The Victorians were a people with high moral standards
The Canadians are a people who enjoy nature and spending time outside.
Note the verb that follows who in the above example is in the plural form, it is
"a people (Canadians) who enjoy", NOT "a people who enjoys".
I could, if I wanted, rephrase the sentences so that a people precedes the name of the nation/population/community/tribe etc. This type of construction is not common, but it is grammatical.
As a people the US is particularly patriotic
As a people the Canadians enjoy nature and spending time outside
As a people the Victorians had a strict moral code
However when a people is used alone (without specifying their identity) the verb that follows is in the singular. Taken from an American English writing website Litreactor
You clearly understand more on the topic than suggested by the one
superficial statement I quoted: "Grammar is never wrong or mistaken."
That's a false statement. A dialect is never wrong or mistaken, and a
people is never wrong for speaking a minority dialect, even if it
brings unfair bias and persecution against them.
For further details and examples see Longman's People, singular and plural