Even families who are fairly good at managing their money can be fecked.
Everything costs more when you are poor. Often you have no transport so schlepping all over town to get to a cheap retailer can be expensive and time consuming, especially in the holidays when you may have a few kids in tow. You are therefore reliant on more expensive corner shops.
Your energy costs may be higher as you live in a damp poorly insulated house and are on a payment meter.
If you need to borrow money or buy a new appliance, you can't easily whack it on a no interest credit card, you are paying top rates of interest/hire purchase type schemes.
You may have never have learned to cook budget food well because of the way you were brought up.
and that's before you even get to the issues of alcoholism, gambling, drugs etc.
For every family that people perceive to be coining it in on benefits, hundreds and thousands are struggling.
As for part time work, apart from the issues already mentioned in terms of the effect on benefits, there is also the fact that people with money to spend on things such as house-sitting and dog walking may not be immediately amenable to handing over their house keys to "poor people" as they may not trust them not to rip them off - sad but you can't necessarily blame them.