Brother, you misunderstand. I am not talking about us "doing it alone." I'm talking we can't do it at all.
It is not that we do not obey at all, it is that our obedience is of God and not of us. Of course the result is our obedience and our willingness - but, as Spurgeon once illustrated, we are saved willingly against our wills. God works within our wills to change us. But this is not cooperation and we have absolutely nothing to offer.
If this were true we would never sin as Christians and there would be no need for ongoing sanctification. However, the fact is we do struggle even as Christians with sin. Paul confessed his own struggles.( Romans 7:16-20) We are commanded as Christians not to grieve the Spirit. (Ephesians 4:30)
So it is clear from scripture that while we do not do it alone we bear some responsibility to respond to the commands of God. We respond to salvation by acceptance, belief, trust, faith, and confession. (Romans 10:9-10) We respond to God in ongoing obedience by submission. Paul talks about this in Romans 8.
The only thing that could be produced via your theology is perfect Christians who never struggle with sin and only ever make perfect choices.
Our response to God is not a determining factor of who gets the credit for our salvation and sanctification. Only He who has the power and authority to give it may receive the credit regardless of whatever response God may require from us.
Our response does not, in fact, mean we are relying on ourselves for these things. It means we are in fact relying on God to accomplish what we could never do without Him.