Also what effect would more people voting lead to the current two party system? Could a true third party live with the more voters or not?
 
Voter turnout is low for a variety of reasons listed so far and a couple not yet mentioned.
1) Difficulty: Resgistration is unecessarily difficult. Voting takes place on an inconvenient day and is often at an inconvenient location. Other structural impediments such as voter ID laws add to the difficulty. And there are high levels if disenfranchisement. Finally, elections are frequently poorly organized and run by ineffective volunteers.

2) Lack of Percieved Stake: Many potential voters don't believe their vote will be effective in producing a desirable outcome. Either they don't see a party that represents them or thete is a lack of trust in the system altogether. There's a vicious circle at play here. Low income/status voters don't vote because their interest aren't represented. As a result wealtier voters elect politicians who represnt their interests. And as a result of their interests not being considered, lower class voters tend not to waste their time voting for a choice between two candidates who don't effectively represent them. The two party FPTP system is part of the problem. Also, the primary system and lack of competative races limits participation. And the winner take all EC system also contributes to this.

3) Election Fatigue: Presidential elections drag on and on and on and on and on. And there are too frequent elections.

4) Elective Elections: Compulsory voting results in higher turnout.

So, to maximize turnout, we need:
1) compulsory voting,
2) easier and better run voting,
3) a proportional system woth more variety of and more representative choices, and
4) a tighter schedule with fewer actual elections.

I'd add a none of these options as well. Note that with the most recent presidential election, there were ~200 mil. registeted voters. ~63 mil went to the winner, ~65 mil to the loser, ~8 mil went to 3rd parties, and ~64 mil didn't vote. If a simple "none of these" option had been available, it is highly likely that would have been the winner, especially considering the large numbers of voters from either party who very probably would have switched to that.

As to the real question here, it's probably easiest to get some serious electoral reforms in along with the Senate reforms included in the 17th. amendment, circa 1912.
 
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