Is there any method by which the public is able to insist or force a referendum to amend the Constitution or is it left entirely up to the the Politicians?
There are a couple of ways actually!
From the constitution itself!
Thank you for the question:
Article V of the U.S. constitution:
The Congress, whenever two thirds of both Houses shall
deem it necessary, shall propose Amendments to this Constitution,
or, on the Application of the Legislatures of two
thirds of the several States, shall call a Convention for proposing
Amendments, which in either Case, shall be valid to
all Intents and Purposes, as Part of this Constitution, when
ratifi ed by the Legislatures of three-fourths of the several
States, or by Conventions in three fourths thereof, as the
one or the other Mode of Ratifi cation may be proposed by
the Congress; Provided that no Amendment which may be
made prior to the Year One thousand eight hundred and
eight shall in any Manner affect the fi rst and fourth Clauses
in the Ninth Section of the fi rst Article; and that no State,
without its Consent, shall be deprived of its equal Suffrage
in the Senate.
So you can accomplish it via state legislatures or a constitutional convention. The reason the convention hasn't ever been used is that there would be little to no control over what happened at that convention. That would likely end up being a "total overhaul" situation, and isn't ideal. But a single state legislature could put forward an amendment and get 3/4 of the rest of the states to ratify it and then it'd be law. And there doesn't have to be a sunset provision to that, some amendments took a really long time to get in.
There are some that would argue that Congress has to propose the amendment, but don't worry. If the Supreme Court won't enforce an amendment because the process we used ignored "Congress shall propose" then we'll have good precedent for enforcing that "well regulated militia" bit.
The NRA has state legislatures locked up pretty tightly too, but I think we can do it.
Figure: 3/4 is 38 states:
For (maybe with some effort) (18)
Hawaii, California, Oregon, Washington, Nevada, Illinois, New York, New Jersey, Massachusetts, Colorado, Ohio, Michigan, Maryland, Pennsylvania, Rhode Island, Connecticut, Delaware, Vermont
Maybe (with alot of effort) (15)
Maine, New Hampshire, Iowa, Indiana, Idaho, Nebraska, Kansas, New Mexico, Arizona, Georgia, North Carolina, South Carolina, Utah, Wisconsin, Wyoming
Probably better spent efforts elsewhere (16):
Texas, Florida, Missouri, Montana, Alabama, Alaska, Arkansas, Oklahoma, Kentucky, Louisiana, North Dakota, South Dakota, Tennessee, Virginia, Mississippi, West Virginia
Once we get the first 18, the next 15 will be easier, and then it's just enough peer pressure to flip five of the hardest holdouts, maybe compromise to leave veterans with the right or something, and that'll be that.
So unless gun rights activists manage to stop armed rampage killings we're going to amend the constitution with something like:
The language in Amendment 2 is hereby clarified: The right to keep and bear arms refers to the right to possess and wield artificial limbs or strap live bears to your arms. Congress shall pass regulations limiting possession of firearms to peace officers and active duty military personnel, due to the inability of the militia to self-regulate.