If - big if - you considered this, you want to donate money to the school for THEM to pay her salary. Your PTO does not want the headache of being an employer.
Whether or not you provide the funds is up to you. Many of us (the majority, I'd wager) are against PTOs paying for salaries. It's a band aid solution that doesn't usually help in the long run.
But as LuvMyKids said, there are times the PTOs would rather help provide the funds than do without the services.
Does your group have a mission statement? Does this request fit within that mission? For example if your mission statement says "The mission of XYZ PTO is to improve the educational opportunities of our our students." then paying a nurse's salary probably doesn't fit under that mission.
When you say "We don't feel it is our responsibility.", are you talking about your entire membership or just your executive board? Check your bylaws, your board may not have the authority to say "no" to the request. It may need to be put to a vote of the general membership.
I hate to see PTOs having to pay staff salaries, but some choose to do that rather than have their children go without some services/educational opportunites.
Our Principal is asking our PTO to pay for part of a nurses salary and we don't feel it is our responsibility. Are their any legal reasons we can give to turn him down with?