Since many of the sanctions imposed have been the direct result of the Biden administration's urging, I think, yes, you can say that Biden was influential. I also think that the bipartisan response to the first part of Biden's State of the Union speech shocked the world. You could have reliably expected the Republicans to stand up and boo, or at least sit there in stony silence, even if Biden had advocated for fluffy white bunnies, cotton candy, and rainbows. So the world was shown that whatever horrible partisan divides exist in the US, responding to a bully nation's naked aggression isn't subject to such divisions.
I think that that in turn reassured the EU nations that we wouldn't leave them holding the bag if they imposed sanctions--because one has to remember, those sanctions hurt them as well, and to a much greater extent than they hurt us. I suspect that NATO felt the same way that Putin did--that the invasion of Ukraine would send us into a whirl of partisan bickering and inaction. And let's face it--NATO, without the US to back it, can't stand up to Russia. They could hold out for a while, but not long.
There's yet another element in play. Poland in particular may not wait for NATO to get its shit together. No other nation on earth knows as intimately the existential danger of having the Russian bear next to you. If the bear should devour Ukraine, the Poles might expect to be next. The Baltic republics certainly have a similar fear already. So here's a possible scenario IMHO:
Russia is slowly grinding Ukraine down. Civilian casualties are piling up. Poland, even with the help of massive foreign aid, is feeling the strain of caring for over a million refugees. So they decide to send their army and air force, having reached the conclusion that waiting for NATO to do something militarily may be futile--or may take too long.
Poland's armed forces are roughly comparable to Ukraine's in size and firepower. Adding the two together would reduce the ratio of Russian offense to Ukranian/Polish defense from 5:1 to 5:2. And modern military doctrine says that given roughly equal technology between the two sides, an attacker needs a 3:1 superiority to succeed. So a Polish/Ukranian alliance could hold the assholes off, probably indefinitely with NATO and US weapons pouring in.
At that point, Putin just might figure out some pretext to declare victory (a la GW Bush) and get the hell out. We have to leave the carrot of rescinding the economic sanctions in place, but overall, we've been shown that no one can rely on Russia for anything. So, long run, we turn it into North Korea--an impoverished pariah nation.