I'd say it should be under 50%, and completely agree that government in the US (and most countries) is far too large. But I'd disagree about where to cut with most republicans. I think the military budget should be slashed, the DHS dismantled, the public health system properly reformed to be single payer for drugs and services (and thus vastly cheaper), and the political system reformed to outlaw lobbying and corporate support for politicians above very small amounts (to bring them down to the level of individuals). I'd also close tax loopholes for taxing the rich, so that a the tax burden was distributed more evenly. Those measures would reduce your tax burden immensely. This is a hard problem, but so far *no* US politician has the guts to try to address it - there are too many vested interests.
Re healthcare, it's perfectly fine to have private healthcare *for those who want it*, but the gov. is going to end up paying for lots of people in a civilised country, and you should be aware that it would be cheaper for everyone if that was done via a public system rather than the bizarre and inefficient system involving insurance companies that you have in the US at present - I'd abolish Obamacare, and replace it with true public hospitals - like the police service, this is something better and cheaper done by the state to provide baseline care. Those who can afford it can then pay for more advanced care themselves.
I wouldn't get too hung up on how many people pay tax or not though, frankly that's a smokescreen of hate to avoid letting you think about the hard problems - the truth on taxation is this:
EVERYONE, no matter how poor, pays some tax - sales tax, excise tax, fuel taxes, alcohol and tobacco taxes, etc
The vast majority of tax take is always going to be flat taxation and income tax on the middle classes, because that's where all the easy money is
The rich will always find ways to avoid most of income tax (curious that you don't find this a problem?), and thus avoid their share of the burden
The poor will never be able to contribute very much, so your best bet is trying to lift them out of poverty, not tax them more