Your analogy doesn't hold at all. In no way is consent of the governed impossible or analogous to agreeing to be raped, either semantically or logically. Maybe you skipped history lessons, but the whole point of the DoI was to outline the acceptable methods of government to the colonists and to justify the reasons they were declaring independence. The DoI doesn't grant any authority, you misunderstood what I said. The DoI explains the rationale by which the government later granted itself authority by claiming it was acting with the consent of the governed. By living here, you are consenting to the jurisdiction and authority of the government, because you're free to leave. However, you're not free to ignore the edicts of the government, that is "the Will of the People." (Said semi-sarcastically)
Don't misread me. I'm sympathetic to voluntaryists. I'm merely explaining the rationale behind the system of government, not defending it. I think democracy is a rather dreadful thing, as the majority forces its will on the minority with impunity. However, I've never become convinced a completely voluntary society would work, for many reasons which are not the point of this thread.
The short of it is that the DoI does not do the vesting of authority. It explains how and why the vesting of authority is legitimate. The actual vesting of the authority comes from the Constitution.
Consent is impossible because there is no way for me to grant consent even if I wanted to. I don't grant consent by paying taxes because I get threatened with jail or worse if I don't pay. And I don't grant consent by voting because I am not granted an exemption from the laws if I choose not to vote. Nor am I only subject to the laws of the candidate I voted for. And even if I did vote for the winning candidate, the voting was done in secret so there is no way for me to show that I consented.
Just research what the government's own definition of citizen is. It is someone that consents to the authority of government in exchange for protection. Well, using that very definition, none of us are citizens. Newborns are not capable of granting consent and the government has repeatedly said that they are not under any obligation to protect you.
You're taking your unwillingness to grant explicit consent to a government you don't approve of and saying it's proof there can be no consent. I'm not talking about you granting explicit consent, I'm not sure there even is such a thing. I'm talking about the justification of the government in claiming it has consent, which because it does so, creates implicit consent if you stay here. The Founder's claimed consent of the governed in the DoI, and therefore anyone who decided to live under their rule was automatically granting implicit consent because that was stated to be how the government was founded. (In fact, they claimed all governments derive their power from consent of the governed, and the DoI was their notification that they withdrew it from the king. The revolution was them enforcing it).
With how angry the public is at Washington today, there are still enough people who agree that the government has consent of the governed that it makes the government and American society stable. Whether you agree with everything the government does or nothing it does, you grant it consent and recognize it's authority by living in its jurisdiction because you're not forced to stay here. The agreement is implicit. This is how it works; as long as you're here, there are penalties for breaking the laws even when you don't agree with them. If the government doesn't have your individual consent, that's not of much consequence, you can withdraw it by leaving. But if you don't, you can't claim it doesn't have your consent because it does. And if you choose to stay, you're bound by the laws created by the majority. When there are enough people who choose to withdraw their consent, a revolution happens, either violent or not.
I'm not justifying the argument, I'm just explaining the philosophy and logic it's based on. I'm a libertarian and I hate most of the stuff the government does and the way it spends my taxes. But I'm implicitly giving consent because I'm still here. Of course I only pay the taxes out of threat of prison, but the taxes are still "voluntary" because I don't have to live here; I could move and renounce my citizenship and the government no longer has a claim on my income for tax purposes. Because I'm free to do that and choose not to, I give consent to the government and "voluntarily" pay taxes.
You staying is giving implicit consent; that's the bargain. Once you choose to accept the bargain, you don't have absolute freedom to decide which rules to follow and which not. Government has overstepped its role. I believe the only legitimate function of government is to protect life, liberty, and property. But it's not gotten to the point where I would leave. The government can, and does, claim my consent.