It's due to the first past the post system strongly favouring two or few parties per constituency (otherwise if you have two parties that are closer to each other politically, then they're at a disadvantage against the third one.
> The question is: Why can't a new party come up? Is it due to the system itself or the "will of the people"?
I honestly and genuinely don't think that's much of a question.
I encourage you to read Lawrence Lessig's "Republic, Lost"[1] - which talks about how the big money behind campaign financing makes average Joe's feel as if they're choosing a politician based on their will, which turns out to not really be the case. Rather, they're choosing from a select group of politicians already rubber stamped "OK" by deep pocketed donors.
A good quote (not verbatim) from the book is basically how deep pocket donors have a sense of: "Let me choose the potential candidate options, and I don't really care who wins".
So it's the "will of the people" only so far as the people's will aligns with something they have 0 control over - the intentions/ambitions of those with money - which doesn't sound much like free will.
Money has always been integral to political campaigning.
But I'd say the 2016 election clearly refutes your assertion.
Republican fundraising as of 6/22/2016 in USD$millions, {total}, {candidate}, {affiliated PAC} [1]: Donald Trump (67.1, 64.6, 2.5), Jeb Bush (162.1, 35.2, 126.9), Ted Cruz (158.0, 92.6, 65.4), Marco Rubio (125.0, 47.3, 61.8)
If one wants to blame the Illuminati for secretly supporting candidates... this is a harder point in history to find support.
It's due to the voting system. Plurality voting systems tend towards two-party rule. This observation is known as Duverger's law [1].
Now, if the US switched to a radically different voting system today, we probably wouldn't see a flourishing of outside parties tomorrow; it could take a little while. But people sympathetic to outside parties such as the Greens or the Libertarians would be far less reluctant to vote for them if it didn't mean splitting their vote and causing the "lesser of two evils" to lose their local district.