Let's say that someone has made me their Power of Attorney and I don't want that kind of responsibility on my hands. Is there a way to deny it? I am in the state of Wisconsin.
The Wisconsin statute pertaining to power of attorney is here. 244.10(2)(b) indicates that the agent's authority terminates when they resign: there are other conditions, such as if the principle revokes the authority, the agent dies, and so on. If nothing else happens, you would have the authority, like it or not. 244.13 states that if you do anything to appear to accept the position (e.g. make a decision for the principle, or say "Sure, whatever" when offered the job), you have accepted the job. At that point (244.14), you then have to act loyally and with the principle's interest foremost. In order to avoid those bad things, you need to not do anything that can be construed as "accepting". But all is not lost if you say "Sure, whatever". 244.18 provides for agent resignation. Basically, you just tell the principle that you resign, and if the principle happens to be incapacitated, you also inform the guardian, coagent, or successor agent – if there is one – or, the caregiver, or "Another person reasonably believed by the agent to have sufficient interest in the principal's welfare", or "A governmental agency having regulatory authority to protect the welfare of the principal".
But: there's a better way to avoid the problem. 244.20 provides a mechanism for refusing to accept, if you refuse within 10 businss days of being presented with this honor. 244.20(2) spells out when you may not refuse – if you're refusing because of the date of the POA, if it's based "exclusively on a mandate that an additional or different power of attorney form must be used" (these are the lame reasons), or if "The person has no good faith basis for refusal under sub. (1)". To understand that, you have to look for the valid reasons for turning down a POA. Well, there are 9 grounds allowed, and you can refuse the job if any are true. The first one is (a) "The person is not otherwise required to engage in a transaction with the principal in the same circumstances". The remaining conditions are things like "it would be illegal", you have reason to think the document is invalid. I think "I just don't want to" is covered as long as there isn't a pre-existing "but you have to".
Sub 5 provides the possibility that the person requesting the acceptance can get a court order to mandate acceptance, and if it turns out that your reason for refusing was not valid, there could also be their reasonable attorney fees and costs to pay. Because there is a clock ticking, you should note that waiting for advice from a lawyer does not constitute "having refused to accept".
You can not be "made a Power of Attorney." Power of Attorney is a legal authorization that grants authority to an Agent to act on the Grantor's behalf in some capacity.
Because it is not a contract, but rather a unilateral authorization, the Grantor cannot impose responsibility or obligations through Power of Attorney, and therefore there is nothing for a Grantee to "deny."
However, typically some agreement (i.e., contract) accompanies the grant of Power of Attorney, in which case you would be bound by the terms of such an agreement.