An indentured servant cannot leave their employer under pain of imprisonment or death. These folks do not have a choice and must work until they pay off some nebulous debt. Additionally, they have no chance of improving their wages that they are being paid by their employer nor would their employer give them an opportunity to improve their skill set (at least in the historical texts I've read). An indentured servant, under the time that the contract is in place, is little more than a slave. Someone struggling in the US is having a hard time, yes, but they are most definitely NOT a slave.
Working minimum wage sucks and options are limited but the individual can still spend some time to improve themselves. And, they can hop into a new job for an extra buck or two without repercussions. If the person cannot find another means of income due to their own lack of skills then that is on them to a certain extent. But, federal/state governments and private institutions do fill in funding gaps to help poor people develop computer skills, manufacturing skills, etc. Also, if an employee is laid off due to no fault of their own, they have access to welfare. My friend was laid off without due cause by his employer (company tanked) and is currently collecting $2,000 USD a month from the government.
Child support is negotiable and based on salary. If someone is earning minimum wage then the judge is not going to make that person pay the shirt off their back for child support, but they will pay and it will hurt. This is different than an indentured servant contract which is not negotiable. Moreover, in some places the States will give an individual the option to go to jail and the State will pay off the child support for that person while they are incarcerated, one day at a time. This was true in Missouri and multiple dead beats were languishing in jail for months because Missouri was paying $50 a day of the child support. These imprisoned guys were fine with that option and it's a lot better than just getting thrown in jail due to failed payment and the significant other getting nothing. Mentioning jail to further my point is odd, yes, but I think you see the context... even in jail, these guys get a way out of unpaid child support.
On the face of it, people make choices and need money. Sometimes they make shitty choices and can't get enough money to live comfortably but there is not a slave/master-type relationship present like an indentured servant has. The poor person with kids still has some (limited) options to improve themselves and they are not forced to work as a McDonald's cashier for the rest of their life. Although it might seem to the person like there are no options, this is not true. The poor US person living pay check to pay check is in a remarkably different situation versus the Burmese refugee who is indentured to a Thailand fishing boat to pay off his/her debt for being smuggled out of Burma/Myanmar. I think we throw around these analogies too flippantly these days, ignorant of the differences.
I'm not sure how good of a job I did answering you but I took the time to do it so there you go.
TL;DR - The average life of a US citizen living pay check to pay check is a billion times better than an indentured servant IMHO.