I don't see this as a huge issue, although admittedly I haven't spent much time thinking about it. Also, this is not my practice area, but I do like to ponder. I would think off hand that it will come down to how the program is written exactly.
To your first point that the charity is essentially the government, would that matter? The charity is not defined by the work that it does or its affiliations (necessarily) but by whether the organization is a 501(c)(3) or otherwise qualifies under the statute. Case in point, I think there is guidance on donations to libraries (and other similar government institutions) indicating that federal charitable deductions are permitted so long as the donations are used by the governmental organization for a public purpose (which, wouldn't that describe nearly ALL things tax money is spent on?) So I don't think affiliation with the government is necessarily a deal breaker. And I'm not sure that a governmental unit would be prohibited from starting a 501(c)(3) organization for this purpose.
In another vein, can we assume that the organization receiving the money is "essentially" the government? I would assume it would depend entirely on how the credit program is structured. For example, Pennsylvania offers a state tax credit for businesses that give money to certain educational organizations (schools, daycares, etc.). Then in exchange, they receive a 90% or so credit against their PA state taxes for money given to the charitable organizations. If I'm not mistaken, those businesses are still be entitled to whatever federal contribution deduction they would otherwise be entitled to for federal purposes since they are giving to an organization that is a charity. So it's possible California's program could be written in a way to allow people to support institutions (not necessarily governmental) that would otherwise be funded by the government anyway and eligible for a state tax credit.
The quid pro quo idea is one that I hadn't pondered before. But would that come into play if the tax credit is being given by a different entity than is receiving the credit (assuming they are different divisions of the government or like the PA scenario a separate organization altogether)? In addition, suppose I make a donation and then don't have any (or enough) taxable income on which to receive the dollar for dollar credit and I lose it. Arguably, I wouldn't know at the time I'm are making the contribution whether I would actually be able to receive the anticipated benefit -- so then is it really quid pro quo? It's not definite and the value is not immediately ascertainable.
I look forward to seeing other people's thoughts on this, and seeing how it pans out in the end.