The answer is somewhat similar to the "corollary" question, in that this wouldn't be the only information taken into account at a motion to suppress and one would need know why the officer requested (in your scenario demanded) to search you in the first place. There are scenarios whereby he could search you without benefit of a warrant. Was he chasing you from a crime scene? Were you attempting to flee? Did he see something illegal before demanding the search that may have made it legal despite you thinking it not?
The analysis is different if you are in the car versus in your house. That said, regardless of where, a consent search is just not likely to happen in this way.
In your car, the officer has the right to take your keys to "secure the scene," or if there is a reasonable suspicion that you may attempt to flee. Typically, the officer will say "turn off your car" without taking your keys. Despite what's typical, though, they certainly can take your keys if circumstances make it necessary and that (the mere taking of keys) does not constitute a search.
Keep in mind that the police can search a car without a warrant in a number of circumstances, without your consent, that would not be available to them with a dwelling. Courts will typically give police much more latitude to search a vehicle than a home. Under the "automobile exception" to the search warrant requirement, individuals have less of an expectation of privacy when driving a car and there is also a much greater chance of losing the evidence in a car vs. a dwelling, since it's mobile.
Generally, the police can search your car if:
- You have given the officer consent (in this scenario you've not – unless you hand them the keys without protesting – and then this would be considered implied consent);
- The officer has probable cause to believe there is evidence of a crime in your car;
- The officer reasonably believes a search is necessary for their own protection (e.g., they can search for a weapon, if they have reasonable suspicion);
- You have been arrested and the search is related to that arrest (such as for drunk driving or for drugs, they can search for alcohol or drugs).
There are tons of contextually specific rules that dictate when each of these situations is OK, and when they're not, as well as where they can search under what scenarios. It is not a one size fits all analysis. In fact, warrantless and consent searches may be some of the most variable analyses criminal attorneys and judges undertake to explore. The law on these topics is voluminous.
Searching your car after you've given the officer the keys, assuming there was no basis and you actually said "you're not consenting," can result in suppression, but not necessarily as the fight is a lot tougher when it comes to a car. (E.g., if you said no earlier, but then handed the cop the keys later without renewing the objection, this could be considered an implied consent.) Similar to the other question, there is also going to be a whole other side to the story, with evidence aside from your testimony dictating what the ruling will be.
A dwelling is different from a car, although your question makes some assumptions here that I would find very hard to see happening in real life (having represented both police, municipalities, and defendants to criminal searches)....
It would be highly unlikely for an officer to threaten to break in like this ... especially in a dwelling where neighbors and passersby can see what's happening and would not only watch, but would probably video it. This is not to suggest that threats and actual wrongdoing doesn't happen, it's just not typically in this way. Police know the law. They rarely do things so blatantly unlawful that not only will nearly ensure that any evidence is inadmissible, but (in a case like this) where they will also probably lose their job.
Short of a pursuit where the police are chasing someone into a house, I have never heard of a forced entry in a situation like you're describing. While we don't know the circumstances leading to the encounter, I am assuming that the search isn't pursuant to a chase, since you're having a discussion with the officer and if you're chased from the scene of a crime and run into your house, they're coming in. They are not having discussions.
However, since we don't know what the circumstances are that lead to you being approached in the first place, it's difficult to analyze whether he has the right to enter warrantlessly. What we do know is that with a dwelling, it is much less likely to be lawful. As with the other question, the analysis as to whether consent was given or not is far from simple. Suspects are much less likely to give consent to search a dwelling as they are a car, and if they do, the search is often limited to a certain area, so chances of suppression are much better. That said, others will often give consent to the police when requested of them (spouses, kids, landlords, hotel owners, etc).
Just imagine ... there are literally thousands of warrantless searches done every single year in the U.S., nearly all of which are alleged to be based on some form of consent. Assume every one of those people has a lawyer; that means nearly every one of those cases is arguing the consent was bad, some way, some how. Duress is one of the most common arguments when someone gives permission; either explicitly (like what you are proposing), implicitly (they came with 10 grimacing cops, so the guy thought he didn't have a choice). Most of the time, however, there is no duress, people just simply didn't know they can say no, or they think the cops won't find what they're hiding.
Cops can do a lot of things to get you to allow for a warrantless search. They can even lie to people to get them to consent, and officers are not required to notify the suspect that he has a right to refuse to consent (however, telling the suspect they have the right to refuse is helpful to rebut the coercion argument). In United States v. Mendenhall, "The fact that the officers themselves informed the respondent that she was free to withhold her consent substantially lessened the probability that their conduct could reasonably have appeared to her to be coercive."
Keep in mind, a big part of the reason why these scenarios are unlikely is not just that the police can find a way in that won't be so challengeable, if they really can't get a legitimate warrant and need to find a deleterious way in. It's also because 9 in 10 times when a police officer does a consent search, the suspect signs a consent form. That's not to say that people don't get coerced or get searched due to duress, they do. But typically not in so blatant a way. There are shades of grey in most of these cases. So, to answer whether you can get the search suppressed if it leads to an arrest under these facts; the only answer that is definite, is that nobody can be sure.
If consent searches, their exceptions, and all ways the evidence gets in and the evidence is kept out interests you ... read these two law review articles. There are probably 200 cases footnoted between them!