Nobody starves to death in the US. Nobody is denied medical care in the emergency room. In many places (though not everywhere), there are shelters where a person can sleep inside. There are food stamps and a patchwork of welfare programs.
However meager they may seem, things like this amount to a form of universal basic income. Does it prevent people from working?
In some cases, you could say it does--there are populations in every city that survive off this safety net, though they don't live well.
But in most cases, it doesn't prevent people from working. The vast majority of people are willing to work for a better life than what the US "basic income" can provide.
What makes you think this would be any less true if the basic income was, say, $30k per year instead of whatever the equivalent is now to provide the meager safety net we have?
It's certainly possible to survive on a $30k basic income in many places in the US, but for most, it won't be an easy or especially pleasant life. Most people will want better.
With a basic income that's a bit more substantial (and has no strings or stigma attached), people will have more freedom to make choices that can truly improve their circumstances, rather than being stuck on a treadmill of barely making ends meet with no space to come up for air and consider education or career changes.