I knocked one together for the UK, if it helps. But it is 'back of napkin'. There are all sorts of details you'd want to fill out. Here:

[There were requests for "back of a napkin" calculations, so I've done some for the UK. To convert to USD, just add 50%, as a rough measure.]

tl;dr - About £80 a week seems roughly achievable as a starting point.

Firstly, I'd like to say I prefer thinking of this as a "Citizen's Dividend" rather than a "Basic Income", as the latter suggests it's useless if it doesn't cover a persons cost of living. I think even a small start is better than nothing, and it can be increased up to become a Basic Income in time. I'll refer to it as BI (Basic Income) here though. So, let's see what we've got...

The UK government spends £732 billion. If we subtract £222 billion for Social Protection (we're replacing all of it with our BI), we get £510 billion required. If we add up all government income except Income Tax - Business Rates, Excise, etc - we get £481 billion.

That leaves us a shortfall of £29 billion. For the sake of simplicity, I'm going to assume that reductions in crime, the increase in VAT revenue, better health, etc are going to cover that. Let's call it close enough for government work. At the end of the day, we currently borrow £84 billion anyway, so at worst I've slashed the deficit :-)

Income Tax brings in £167 billion. UK population I'm going to take at 60 million. So, as a starting point, that gives us a BI of £2,783 annually, or £54 ($80) a week. Well, that's not a bad start! Let's consider what it means for actual people. Thus far:

Who loves me:
- Right-wingers. I've eliminated (or vastly reduced) the deficit, effectively increased the income tax allowance by £2,783 and given them this amount in cash, while reducing welfare payments to lazy, single-mother immigrants. I should be head of the Conservative party.

- Most people on Job Seekers Allowance (unemployment benefit). While I've cut the amount they actually get, I've also cut out all the paperwork, visits to the job centre, taking money off them if they happen to earn something that week, etc etc. Money without the hassle.

- Low wage workers. This is a big boost above Working Tax Credit and is hassle free (you don't lose it by earning more). It also allows some degree of security in the event of losing their job.

Who hates me:
- Left-wingers. While I've helped some low paid workers, I've also slashed benefits, there's no housing support...in short I've cut welfare while giving more money to wealthy people. I should be head of the Conservative party.

- People who're claiming several benefits. People who're on sickness benefit. Basically, all the folk who've had their income reduced below a living wage.

- Pensioners. The state pension has been cut significantly (and illegally).

Ok, I think I need to balance it a bit more. I'm going to reduce the Income Tax allowance from £10,000 (current) to £6,000. This should balance out at the end. I'm going to assume this increases income tax revenue by 25% (I've no idea if this is remotely close. If anyone can be bothered finding out, please let me know). More controversially, I'm also going to increase income tax by 25%, so the basic rate is now 25% rather than 20%.

That should give me a total revenue increase of 50% from Income Tax which gives me a BI of £4,175 annually or £80 ($120) per week.

And I think I'll leave it there. We'd need to borrow (or cut spending elsewhere) to make up other shortfalls (such as pension payments), but as long as it's less than £50 billion we still come out ahead. It might be more natural to cut the payment to £70 for everyone in order to free up some cash for other payments. In the real world, you wouldn't exclusively reserve Income Tax to one specific spending area anyway, but it makes things simple enough to get a rough measure.