What you are talking about is job guarantee.

Here's the problem with job guarantee:

1. Who defines work? Is raising a child work? What about devoting oneself full time to the arts? Who decides who is able to work? Note that people die while fighting for disability in our current situation. Do people have to take any job they can get/do, as is the situation with a lot of workfare programs? How long do people get to find a new job?

2. What if there is not enough work to go around? Do we invent makework? How do you achieve 100% unemployment. In part, this could be eased by defining full time parenthood, volunteering, etc, as "work."

These are major flaws in job guarantee that do not occur if you just go all the way and guarantee a living income to all citizens (that covers expenses but few luxuries) regardless of whether they work or not. Pilot programs have shown that the majority of people will continue to work, and that employment only drops for new mothers (A baby is work) and high school students (Going to school is work).

Job guarantee also perpetuates the wage slave inequity. When losing your job equates to a very real risk of death, all the power is held by the employers. Unions help mitigate this but history has shown how easy union busting really is. Basic income, on the other hand, means that any citizen is free to leave their job at any time, which gives them increased bargaining power. It would also replace all existing welfare programs except for extra assistance required by the disabled and chronically ill. Job guarantee requires infrastructure to ensure people are "working" by whatever definition you use.

Our current system is profoundly broken. But when we contemplate replacements we need to thoroughly think them through so that we can see where they might break and, ideally, fix those problems proactively.