What would work, I think, might be a phase-out: for anyone who's getting less in SS payments than the UBI, just replace their SS with UBI. For everyone making more, they don't get a UBI, they just keep drawing SS. (Or, you could say they get UBI plus the difference between SS and UBI.) Then eliminate the SS portion of the FICA tax and stop everyone from paying into it going forward. Then there'll be some math involved in figuring out how much people who partially paid into it get, but the end effect is that SS will cost less and less money until finally everyone's aged out (to the point where the amount they'd draw is less than UBI so we can just cancel SS altogether). It'll cost a bit more in the short term to do it this way, but it's more fair to people who paid into the SS system and it won't get the AARP voting against you.
>Edit / Afterthought: No one currently receiving social security or unemployment will support this proposal because they are all receiving way more than that. More than 700/month, and certainly more than they need to survive.
Again, you'll have to phase it out. Unemployment is an insurance program that people have paid into, just like SS, so of course they expect it to be there if they need it. And it may (or may not, depends on the person and their income) pay more than they need to survive, but if they have a lot of expenses like a big mortgage then that's irrelevant. They've been forced to live in a society where having a job is basically required for survival unless you get on the dole (which prevents you from working, so it's a trap), so unemployment is something the society has created to mitigate risk.
But like SS, it could be phased out (and the taxation from that eliminated). It could probably be replaced with privately-run unemployment insurance though, but it wouldn't be as necessary with UBI.
But your $700/month sounds low to me. I know it's supposed to be a bare minimum, but even that seems too little to me to live on with today's rent prices. I do think the government has a responsibility to do something about that; rents have been driven up far too much by Wall Street, foreign investors, speculation, etc. UBI needs to be enough for someone to live on with roommates (and not more than 1 per bedroom at market rates), in an average cost-of-living area, plus reasonable grocery store bills and a bit extra to cover transportation costs. If it isn't enough for that, it won't work, and it needs to be jacked up until it is. If that means instituting a big tax on Wall Street, then so be it, since they're largely responsible for the cost of living being what it is.