Some of us (myself included) are guilty of adding these things onto the end of that verse. "I can do all things except...
-stay on a budget
-keep my house clean
-give up cable TV
-stop eating chocolate
-stop itching mosquito bites
-sponsor a needy child
-be a missionary to a foreign country
-be a missionary in my own neighborhood
-discipline my kids consistently
-cook meals for my family instead of eating out
-fill in the blank with whatever YOU "can't" do
If you try to do it without God, yeah, you'll fail. If you ask for His help and continually seek Him , He will give you supernatural power. From the smallest thing to the largest, He can help you. Don't say "I can't", say "With Him I can".
It's only by the grace of God that we do anything.