They can 100% tell you verbally through the door "You are under arrest," and at that point, staying inside your house is obstruction. This idea that by making it physically difficult for the cops to put their hands on you, you're putting yourself in a better position legally or practically, is 100% wrong. They are well prepared to deal with physical obstructions. In general, being antagonistic to the police or putting obstacles in the way of them doing basic things like talking will motivate them to make your life more difficult, which they definitely can do.
Personally, I think people place way too much emphasis on the "arrested" part of the equation and way too little on the "charged and building the case" part. If you stay inside, they leave and issue a warrant for you because they never got a chance to talk to you, and then pick you up later, for example, you've gained absolutely nothing. If you step outside, they arrest you, but you didn't manage to add any charges with how you handled yourself and didn't give them anything to help them build their case, then that's about the best outcome you can have. Crucially, I think encouraging people to be physically obstructive with the cops tends to build habits that can serve them very very poorly in the future.
If you don't believe me, here are some law offices' professional explanations, which honestly are kind of better than what I said. What I said is just a clear simple guideline based on my understanding.
https://sieronlaw.com/posts/when-police-show-up-at-your-door/
https://www.snaderlawgroup.com/dos-donts-police-door/
Again, all of this is kind of fluid or no longer accurate right now anyway, because the rules are changing. In the current climate I would start to lean more towards just not answering the door at all, but a lot of it depends on what agency they're with.