All true. (An NBC-Wall Street Journal poll released late last week showed that twice as many people have a negative impression of Cruz as have a positive one.) And all irrelevant to Cruz at the moment.
Consider this for a minute: What if you told Marco Rubio, Chris Christie or Rand Paul that you could increase their chances of winning the Republican nomination but, in so doing, you would lessen their chances of being elected president in the general election? Don't you think all three of them -- plus any other candidate mentioned as a potential 2016-er -- would take that deal? We do.
That's exactly what Cruz has done over the past month or so. No one -- not even those who hate Cruz -- can doubt that he has emerged as the face of the uncompromising Republican opposition to President Obama (and his health-care law) since talk of the shutdown and raising the debt ceiling began. His 21-hour filibuster against Obamacare is a touchstone sort of moment for rank-and-file Republicans, the kind of principled stand they will be talking about for years to come. If you want to elect the anti-Obama in 2016 -- and lots of Republicans will -- Cruz is positioned to be that candidate. And, if Obamacare's current struggles continue and the law is seen as a major mistake in a few years' time, Cruz is the face of the "I told you so" wing.
In politics, you cross the bridges as they come to you. Worrying about the next race before you win the current race is a recipe for disaster. (Remember how George Allen was focused on running for president in 2008 during his 2006 Senate reelection race? Whoops.) Cruz's thinking almost certainly goes something like this: Winning the Republican primary is the goal. Anything after that I'll worry about when I get there.
While polling would suggest that Cruz's appeal to the Republican base has come at the expense of his potential appeal to the broad center of the country, general elections for president are heavily influenced by environmental factors like the state of the economy, the public's optimism/pessimism and the relative brands of the two parties -- factors that are tough to know this far in advance of the race. That's not to say Cruz would be a surprisingly strong Republican nominee -- all indications are that he would struggle to broaden his support base -- but rather to say that drawing hard and fast conclusions about an election more than three years away is a fool's errand.
Ted Cruz doesn't care about the 2016 general election yet. Nor should he.