I say a lot of stupid things. But I hope I never claim to be "basically a single parent." I've heard women say this when their husbands are traveling or sick. Being without your spouse for reasons of work or illness for weeks or months at a time is not, in my mind, being a single parent. Having grown up in a home where my parents did not live in the same house for 8 years (2 living apart, 5+ divorced) I take exception to this complaint. It's like someone who is feeling sick saying they "basically have cancer."
Single parents are single for a variety of reasons ranging from death of spouse, betrayal of spouse, never had a spouse. And single parents provide for themselves through various means, from child support, government aid, full time work. While some single parents retain the support of a co-parent that can provide assistance with child care, financial support, or other, they aren't a spouse.
So I think my main beef with this complaint is that to me single parents are not married, and these women are married. And while these women are stressed out by a temporary time of increased burden on themselves, they still have a spouse to share the burden with when they get back from travel, or sickness. This complaint denies the true difficulty faced by people who are actual single parents and expresses ingratitude for the marriage that is still intact.
What I would like to say is "I'm sorry that you don't have the support of your husband right now. I hope your marriage continues to bless your lives."