The honest truth is that there are times I still don't know if I can handle a large family. I am not naturally patient or organized or energetic. I like to have time to myself, and I don't like to be interrupted.I am selfish and grumpy and sinful.
None of those this is conducive to mothering a large family.
But through a series of events and conversations and readings , I came to realize a few years ago that I can actually grow in patience and develop organizational skills and outgrow my selfishness. And I came to see children as a blessing from the Lord, just like the Bible says they are. 
I also saw through reading the scriptures that God uses weak, imperfect people to accomplish His purposes, and that He provides the means and the strength to carry those purposes out. (See Moses, David, Jonah, Joshua, Peter, etc.)
God tells us many times in scriptures that He will guide us, care for us, protect us, give us strength, if we trust in Him.
I've got the weak and imperfect nailed down, so once I put my faith into action, and I must do this daily, then I know I can handle a large family.
Don't forget to read about how the rest of the 4 Moms of 35+ Kids  know they can handle a large family.