Your job income adds directly to those $2800; it does not replace the basic income. E.g., if your employer pays you $500 a month, your total monthly income will be $3300.
Note that life in Switzerland is expensive enough that $2800 is not a whole lot more than minimum wage level in the US.
And that's perfectly fine. It's not like the employee would starve. You'd still have to pay enough so that working for you is worthwhile (because people aren't forced to work or starve). Employees would have the genuine bargaining power of a free agent, because employment would no longer be an existential need.
Also, it would be much easier to become self-employed or become an employer yourself; not only is the risk of failure lower, but your payroll expenses would shrink enormously. If there were a basic income, I'd have started my own company long ago (or at least tried).
Note also that "keeping more to yourself" is modulo the higher and more progressive taxes you'd need to finance a basic income.
The big question is rather: would enough people still have an incentive to work? It depends, I think, on how close to the subsistence level such a basic income would be.
That's my other concern. $2800 a month isn't enough for me personally to be able to stay home and play video games all month, but it might be for a fair number of people. And they wouldn't be contributing much to the economy (other than to the makers of Cheetos snacks.)
Here in Québec, we have "social help" where the government gives you money if you cannot work, etc.
A lot of people I know abuse of this. Pay the rent with the social help, then get money "under the table". A lot of people abuse of it, but I still think it's worth it. I work hard, but I know that if all else fail, I won't be stuck in the street.
It's also not a perfect solution. There are still homeless people (who are often too ill to be able to ask for the social help, or don't have a permanent address to sent it to). You can't live very well in Montreal with it alone, but you can manage to get somewhere to live, especially if you have "sidejob". Otherwise, there are HLM (French for "housing at moderated rents") where the rent is actually based on your income. You can live for $350 - $900 / month in a three room apartment in those. Especially if you live around the island on Montreal and not on it.
People who use this service are frowned upon. They call them "BS" (Guess you would call them SH in english, for "Social help"). The stereotype is that they all abuse the system, take your hard earned money and live in a big appartment with the latest computer, drink all day (no work!) and do drugs. People fail to see that computers are not as expensive as they were before.
I actually grew up in that world. The abusers were a minority. A large, noisy minority, but a minority nonetheless.
So? We don't have enough jobs for everyone anyway. Instead of guilt-tripping people by telling them it's their fault for not having a job and then making them jump through hoops to get unemployment, let's just cut everyone a check and let them eat Cheetos.
And there will be an extra kick to the young, whose labor is less valuable.
A negative income tax or EITC tends to work better, since you have to do some kind of work to get them. And the best way of determining if someone has a job tomorrow is if they have a job today. Long-term unemployment sucks.
The employer has to pay enough to get people to bother to apply for the job. If it can convince people to come into work while paying $1300 instead of $2800, then why not let it? We don't have to worry about people being forced into a job they hate, because they've got their basic needs cared for. Employer gets cheaper marginal labor, employee gets minimum income plus more income plus lower effective marginal tax rates.
You put your finger right on why this was originally a Republican proposal. It would replace the minimum wage, and allow the wages for low end jobs to go as low as would attract anyone interested in earning something above the mincome level.
Note that life in Switzerland is expensive enough that $2800 is not a whole lot more than minimum wage level in the US.