I've experienced both types of VA offers and unfortunately, it just encourages the practice of accepting and then withdrawing part way through the onboarding process, which I've done. I wish I didn't have to but ya gotta look out for yourself.
If there's one thing I've learned about myself (and most of my colleagues who went into the 'helping' profession of clinical psychology), it's that we don't 'look out for ourselves (and our own interests)' nearly enough. This can be tied to under-valuing ourselves as well. If we're not careful, we can get into work 'relationships' that are exploitative and that also undervalue us.
Not saying that dynamic is operative here, just something to consider. On the face of it, the fact that they are pressing you to make an immediate decision ("We're extending you an offer to commit to us but OMFG you must do so within 24 hours or else!") is a sign that--quite possibly--they are either (a) trying to get you to commit to something that, upon further investigation, may not be the best deal for you (why the urgency to commit immediately?); maybe it's a CRAPPY position that they can't get anyone in their current organization to work in because people are burning out in that position and the word is out; (b) engaging in a dysfunctional dynamic where they have all the power and are just expecting you to have some personal schemas operating in the background of your mind something to the effect of ("I'm not worthy, I'd better take this opportunity while I can before I miss out on it"; or "They are acting dominant and pushing me to commit (as if they have something of value that someone else will come along and take if I don't act immediately and I will miss out (and be a loser, etc. etc.))"; or (c) your position in terms of what you have to offer as a candidate employee is better than what they are offering and they are--therefore--employing high-pressure scummy sales tactics (e.g., the late night TV commercial that offers you a special deal if you 'act now!!!' within 24 hours!!! or miss out on this great deal' sort of thing.
Of course, it could be none of the above. It could be that (shocker) the people in charge of making these decisions are lazy, incompetent, and representatives of a system run by such folks such that they can't/won't tolerate the uncertainty of weathering a reasonable time period (6-8 months?) of undergoing a thorough, careful, and resource-intensive job applicant search in order to secure the best candidate---they want the uncertainty to go away as soon as possible and that is the top priority (e.g., getting SOMEBODY to fill the position so we won't have to worry about it anymore). These organizations are taxpayer funded, have no market competition, and, therefore, don't have to make smart or effective business decisions. If they--another shocker--run a system that sucks (since they have no competition and just ask congress to fund a 20 billion dollar increase to their annual budgets), then so be it. The bottom line is making the boss bureaucrat happy.
Of course, it COULD be that it is a highly sought-after (by applicants) and desirable position...but if so, you have to ask yourself why they are having any difficulties at all filling the position 'in-house.' I dunno, just something to consider.