My H falls asleep at the drop of a hat, too.

I don't know what to tell you about the pressure. Of course there is going to be pressure. Married couples make love.
That is a fact. She is beating herself up for not doing her part and then blaming you for the supposed pressure you are putting on her. What pressure? You're married to her, that's all. And married people have sex.

I have had some success in having the following convo with my H, but I don't know if it would work with your H:
What time of day would you like to have sex?
He: Well the mornings I am too busy getting ready to go to church. The evenings I usually fall asleep. The afternoons are consumed by the kids. So I don't know what to say.

Me: Well there has to be a time and I need to know what chunk of time you are willing to carve out a spot for me and making love.
He: Well I just told you about my day.
Me: I heard you. I am asking you to tell me where we are going to tweak that schedule, in order to be able fit it in.
He: wh....uh...er......

etc.

It had simply never occurred to him that he would have to make changes and that these excuses were not valid within the context of marriage. As you say, you are NOT her roommate.

This is a rather hard nosed approach and I don't know that it would work with a woman as it did with my H--who is a tell it to me straight kinda guy.

But I think the message needs to be communicated to her in some fashion--it is simply not acceptable and won't work in the long run (for the M) to write off sex. You love her, you will think of a way to phrase this that doesn't sound so harsh.

Perhaps something like: What are you willing to offer me in terms of our sex life? What changes are you willing to make in order to be able to fit some couple time into our lives?

If she says "nothing", then you will know it is time to schedule some counseling.

Btw, do you meet her needs sufficiently?

Honeypot