401K withdrawal are considered unearned income, similiar to interests earned from bank deposit.
It is not earned income that is needed for ROTH.
Of course you can easily work 4 weeks to earn income up to $6500 to contribute to ROTH, the problem is that you will pay social security tax on it, in additional to income tax. Let's say you give your child $6500 to "hire" you as babysitter, that's earned income. But your child as employer has to pay 7.65% social security tax for you, and you have to pay the other 7.65%. So you and your child has to pay 6500*15.3%=$994 social security tax in order to get $6500 earned income reported as eligible for ROTH contribution. Actually I think the employer's share of 7.65% doesn't count as your earned income, anyway, you get the idea.
However, if you only earn $6500 well below the $22850 limit, your social security won't be impacted. Only earned income above that limit will result in reduction in your social security payment.