The short answer to your question is: So long as no major changes are made to the structure of our government and the voting method which we use to select winners for seats, no, it will not change.
Consider Duverger's Law. The U.S. government's organization and method of choosing candidates to fill seats greatly discourages the co-existence of more than two major parties, as any similar government organization is inclined to do. The U.S. government has single member districts or seats rather than proportionally represented multiple-member seats, and these seats are filled using the "vote-for-only-one-candidate" plurality voting method. Any government that possesses these two traits is very likely to be comprised of only two major parties. This behavior of governments was originally studied by a French sociologist named Maurice Duverger and is consequently named Duverger's Law.
From Wikipedia site:
"A two-party system often develops from the single-member district plurality voting system (SMDP). In an SMDP system, voters have a single vote which they can cast for a single candidate in their district, in which only one legislative seat is available. The winner of the seat is determined by the candidate with the most votes. This means that the SMDP system has several qualities that can serve to discourage the development of third parties and reward the two major parties."
If Duverger's Law is indeed correct, then other hurdles typically blamed for stalling third parties such as financing limitations, corporate influence, electoral college method of electing a president, voter apathy or ignorance, poor media coverage, ballot access laws, etc, are not primarily responsible for locking the U.S. electorate into two-party dominance.
The way I envision it, the single member district plurality voting system in the U.S. erects an essentially impenetrable wall for third parties. On the other hand, third party burdens (eg. ballot access laws) are only hurdles that could be overcome with some effort once the wall has been removed. We need to get rid of the wall first, then attempt to remove unfair burdens like ballot access petition requirements.
In my opinion, the simplest and most effective first step of knocking down this wall would be to replace the worst of all voting methods, plurality voting, with something much better like range voting, approval voting or perhaps a Condorcet method. These voting methods give each voter the opportunity to cast a ballot for multiple candidates.
The very constraining rule that holds voters to only one candidate encourages vote-splitting and "spoiled elections" and therefore unfairly and unnecessarily discourages a voter from supporting a favorite third party candidate. In essence, this "vote-for-only-one-candidate" rule is a major component of the impenetrable wall for third parties.
In the event that this simple voting rule change is not adequate to bring about a multiple-party government (creating proportionally represented multiple-member districts also may be necessary), at least it is a step in the right direction, and many other benefits would be realized by using a much better voting method than plurality.