I am glad that you brought that up. I am very aware of the limitations and time constraints of fertility. My husband and I married in our very late 20's. He was entering graduate school and I was working. Having "finally" found the opportunity for marriage in our almost 30's, starting "early" was not an option. And being older, we already had financial responsibilities that weren't going to take a pause so that I could quit work, raise babies, and magically come up with money for his schooling.
He had student loans & tuition to pay and I had already bought a house (which turned out a blessing since it was cheaper than rent). Those things and our remaining needs had to be financed in some way, so I worked. My job required a significant amount of travel, so in order to make children a reality, I started looking for a job that would allow me more flexibility. That took over a year and I then would have to take a significant pay cut. We tried to make our budget work with that pay but adding the cost of childcare and the numbers just weren't going to fit so I kept my existing job. Currently, my husband only had a little over a year left in school so we decided to give kids a go and that we could make it work. My works generous maternity leave program will give us a good buffer if it works out that way and my parents have moved to our town so they could help with childcare if needed. Is it ideal? absolutely not. But it will be good enough and my husband will soon be able to enter the workforce again to ease our burden.
The only reason I tell you all of this (and you can pick it apart all you want) is because maybe I did want a particular number of kids, but sometimes circumstances and timing just simply don't allow for it. We make our choices based on limited information about our future and a little trust in personal revelation. I'm well into my early 30's and my circumstances probably won't allow me to have what I initially wanted. And that's ok. I will count us blessed even if we can't even have one child. Could I have made other choices? Of course. I could have quit my job and had my husband take out massive student loans to pay for our needs. And I could have then probably gotten medicaid to pay for the hospital bills and foodstamps to ease the grocery burden. Would that have been a good decision? I say no. No one else has the responsibility to pay for what I want. "Want" is simply not a good enough reason.
But, I don't think people who choose gov't aid to have kids are necessarily bad people who are disobeying counsel. I think they have their heart in the right place, I just don't agree with their ideas behind making it happen or their interpretation of the two counsels (self reliance and having kids).
Hopefully, you don't think I'm morally preening for pointing out that the two counsels don't have to contradict. It has been my experience that the moral preening has come first from those who have children via help from medicaid and other welfare programs. In my ward, when the topic of children or family finances coming up someone starts going on about how great they are for their struggle. I hate it when people act like exclusive martyrs.
My ward is in a college town, so we have tons of masters and phd student families. A few weeks back, a guy flat out said "Couples who are delaying children due to the financial strains of education are following satans plan to destroy the family." Then, another guy chimed in "Yeah, you just pop 'em out and Heavenly Father will make the rest of it work out for you."
Oh dear no. I had to say a little prayer for strength not to lash out. So, that's where I'm coming from.
I think the moral of the story for the OP @Doorman is that they have made well meaning choices that have led them to require help. Take the help and do everything to get off it asap. Don't make further choices that make you to keep needing it. You feel bad about it for a reason and that's a productive feeling to have. Take the feeling and harness it to help guide yourself to self-sufficiency. Keep on keeping on and you'll be fine!
And not that he's going to, but don't be like the couples in my ward and act like your struggle makes you more righteous than those who made choices the avoid needing help. Neither way is going to get you a better spot in the Celestial Kingdom if your heart is in the right place regarding parenthood and self-reliance.