If Obama is a happy fuzzy sweet guy who just wants the best for the world, then he should be in favor of private charity, right?
On the other hand, if he is a sweet-talking socialist, you might read him like Arnold Kling:
In the latter case case, you might be unsurprised that Obama's budget proposal includes a reduction in the deductibility of charitable donations for high-income taxpayers. (I should note that I am employed by a private charity funded by a high-income taxpayer, so I am perhaps biased on the subject.)
On the other hand, if he is a sweet-talking socialist, you might read him like Arnold Kling:
If you want to predict the Obama Administration's behavior, ask yourself what policies can strengthen government and weaken the private sector. That methodology will tell you that private charities are going to come under assault. Charitable organizations offer services that compete with government. That cannot be permitted in a "progressive" state, in which all forms of civil society must be suppressed.("civil society" refers to America and Britain's long history of voluntary arrangements serving many of the purposes of government today)
In the latter case case, you might be unsurprised that Obama's budget proposal includes a reduction in the deductibility of charitable donations for high-income taxpayers. (I should note that I am employed by a private charity funded by a high-income taxpayer, so I am perhaps biased on the subject.)

Comments
If someone in the 35% marginal tax bracket contributes $100 to charity, he gets back $35 in tax relief.
If someone in the 28% marginal tax bracket (who is most likely a more worthwhile person than the 35% plutocrat) contributes that same $100, he only gets back $28! How cold-heartedly regressive!
I, for one, welcome Obama's attempt to bring Fairness back into the tax code. Fairness!
(An equally fair plan would be to allow the 28%-er to deduct 125% of his contribution. I find myself a bit baffled that Obama did not propose this instead.)
The government supports non-profits; SOME non-profits are practically an extension of the government. But, they can't have people giving money to non-profits that haven't become addicted to their grants. They can't CONTROL that money.
Also, I also tend to agree that tax deductions for "charity" (which can be defined rather arbitrarily at times) are dodgy at best. But then, so are many taxes.
TSI is not, by my personal set of definitions, a charitable organization: you don't give stuff away to people who need it. Eventually, you hope to give choice to people who need it, but even then, they'll be buying that choice, not taking it gratis.
TSI IS a non-profit-- I'll take it as read that you consider the terms interchangable, but I, at least, don't.
TSI was formed by a bunch of rich guys, who are actually trying to make a real and positive difference in the world, without making a [monetary] profit off of it. One imagines that there may exist other non-profit organizations, formed by a bunch of rich guys who are not so scrupulous, but are in fact using those NPOs strictly has a tax dodge.
If that is true, then one might imagine that the change in policy put forward by the Obama administration would be an attempt to close those tax loopholes. The fact that TSI gets caught up in the same net, because it uses a system that has been tread by bad dealers, is unfortunate, and might be an indication that TSI could benefit from playing a role in discouraging bad dealers from treading there.
A cynic could easily call TSI "A 'charity' for paying rich kids and sending them on vacations."
If a cynic said that to me, I'd say he had no fucking idea what he was talking about. I'd tell him I quit a job where I was earning roughly 5x as much as I am now and working half as much. Vacation? I think not...
You mean, like the Clintons?
First, there are lots of rules and penalties and audits of what a non-profit is and isn't allowed to do. It's the world's worst tax dodge, trust me. A tax dodge is like a corporate shell in the Bahamas, something that doesn't have to report to the IRS. A non-profit has to tell the IRS why it exists, tell the IRS exactly what it does and what it spends its money on every year, and will get audited if it seems to be doing something to the benefit of any private business or specific set of individuals (as opposed to a general class). I mean, my salary is set by a computer program that crunches all of the non-profit salaries in the US to determine what a fair rate of pay is - that's how regulated non-profits are! Like I said, a terrible tax dodge.
And second, Obama is not changing what types of non-profits are allowed to exist. His budget doesn't do anything of the sort. What it does is make it so that people in higher tax brackets don't get to deduct the entire amount of their contribution. It affects people based on how rich they are, not on what they are donating to.
I'm not saying there isn't plenty of room to argue about what should or shouldn't count as a charity. Your definition has nothing to do with the legal one, but perhaps it is a better one, I dunno. But this is not "closing a tax loophole". Non-profits are not tax shelters, and Obama isn't changing the definition of a non-profit.