I don't think the founding fathers intended for our government to be dominated by two political parties. I attribute it to a lack of foresight of what really took generations to emerge and crystallize.
On some level the "Tea Party" sort of wants a change as well, but they've lacked the discipline to develop and articulate a vision beyond rage. Short of managing a hostile take-over of the Republican party (which they can manage in a handful of races, but "success" requires they do so across the board), they can't accomplish a terrible amount besides mobilize an anti-Democratic base to maybe vote Republican (and then get let down a lot more than they bargained for).
As for Democrats and DADT, DADT relates to an anti-gay government policy. I think this point has been articulated elsewhere, but it is probably necessary for the government to end anti-gay treatment before the government expects private entities to end anti-gay treatment. Furthermore, ending DADT has a lot of popular appeal, so getting DADT repealed should not require the Democrats to spend lots of political capital -- they should be bludgeoning the Republicans for (1) opposing the will of the people and (2) infering with the military's ability to run at optimal levels (this requires that all able and willing soldiers be available to serve -- and given that DADT isn't to be repealed as much as the decision is being deferred to the Pentagon, a body ostensibly suited to the purpose of deciding what gives optimal results will be the one making the decision). However, I don't think the struggles on these issues are just attributable to "pressure" -- for whatever reason, the Democrats and Republicans representing voters are more anti-gay on military service than the voters themselves.
Getting additional influential political parties is probably contingent on changing our Constitution in a way that allows such parties to be viable. If we turned the Senate into a proportional body rather than one that disproportionately represents the individual states, we'd give such parties a voice (and what better body to do it to than the one that currently gives veto power to both major parties). Changing the Presidential election to a popular vote and implementing run-offs for the House and Presidency would give the alternate parties additional openings, but the Senate is the place where they can steadily gain influence before toppling major parties in regional House elections and then finally contend for the Presidency. However, the power to commit to this sort of change is held by the very people we want to hold accountable.
