Because the population of the country is going up, nearly every election has more voters than previous elections. But if you look at the percentage of the population voting (http://en.wikipedia.org/wiki/Voter_turnout_in_the_United_States_presidential_elections), it's been around 55% since 1920, and in fact the percent of the population voting in the last two elections (over 57% both times) was higher than any election since 1968. The two Bush Jr elections were 51% and 55%.
What's also striking is that elections before 1900 had around 80% voter participation, then it dropped to below 50% (1920, 1924), then has been roughly level since then.
So (1) people aren't voting less now than in previous elections - if anything, voter participation is higher than it's been in decades. And (2) what happened in 1900 that changed voting so dramatically?
As for it being a bad thing if everyone votes, the US is a Democracy based on the legitimacy of the elections representing the will of all of the people. If enough people stop voting, the elections, and thus the country, lose legitimacy. That's why most people think that it's important to encourage voting, by making it easy to register to vote, by having enough polling stations for people to vote, etc., and they tend to regard moves to prevent voting as un-American.
And as for the relative number of (self-identified) Democrats and Republicans, the numbers are well known (e.g. http://www.gallup.com/poll/159...), with Democrats consistently outnumbering Republicans. The only time that Gallup has ever polled Republicans leading Democrats was in 1991, when Bush Sr's popularity was boosted shortly after the Persian Gulf War.
So how does a minoritory part retain power? By manipulating the game. For example, Republicans' gerrymandering managed to give them control of the House despite their getting over a million fewer votes than the Democrats in House elections.