It would not bother me in the slightest if God turned out to be less powerful than is routinely claimed within the Church's liturgy and doctrine. In fact, I would delight in it as it would emphasise the personhood of God. That God is capable of doing the impossible seems illogical to me. Surely if God can do something then it is a possibility. Therefore, God can only do that which is possible. Acceptance of this leads to two choices. Either anything that God can imagine doing is possible for God or only those things that can be done according to "the rules" are possible for God. Both options allow for an all-powerful God (being able to do everything that is possible is the only thing requisite for all-powerfulness) but the possible nature of that which exists is potentially very different depending on which of the two is true. For example, a god who could do whatever can be imagined by that god could build a planet out of ice cream and have it orbiting its star, without melting, at a distance of just one hundred miles. However, a god who has to abide by the rules of creation could not do this because, within nature as it is, such a planet could not be made in the first place (interplanetary gas and dust are not dairy products) and it would most certainly melt if it was placed so close to such a massive heat source.
Personally, I hope that the latter of the two gods is the real God. It is more logical and it would help answer such difficult theological questions as "Why does God allow bad things to happen to good people." To put it simply, God does not stop the earthquake because God cannot stop the earthquake. This would not be because of any lack of power on God's part but because it is not possible, according to "the rules," to stop an earthquake and God cannot do the impossible because if God did it would not be impossible. I love the idea that the Goldilocks principle that states that for a planet to be inhabitable it has to be in the "just right" location also has a theological reality. That, for life on earth to be as it is, it required God to create the universe dependent on physical laws that make that life, our life, possible. Earthquakes are usually caused by shifting tectonic plates and the movement of the earth's crust over the molten core of our planet is one of the most important contributors to the earth being "just right" for complex lifeforms to exist.
If God is only capable of being able to do that which it is possible to do due to the very nature of things we would be able to get rid of all the predestination nonsense from our theologies. Time travel may or may not be possible. However, most physicists who believe it might be do not believe it is possible to travel forwards in time because the future does not yet exist. There is no future to travel to so it is impossible to travel into it. You cannot eat a loaf of bread until it has been baked. God cannot do the impossible (because if God did it would not be impossible) so God cannot travel into the future, so God cannot see into the future. God may be able to predict what is going to happen in the future very precisely because of an awareness of all that has happened in the past and is happening in the present, but that is not the same as knowing exactly what will happen in the future. God has created far too complicated and unpredictable (see quantum physics) universe for such prescience to be believable. Even the claim that God lives outside of time does not alter the situation as time is only that which has happened and what is happening. There is no future time to live outside of as it does not exist.
If I am correct what would it all mean for us?
For a start it returns our free will to us which has recently been under sustained attack from philosophers and neurologists. Secondly, it makes us responsible for our futures. Thirdly it let's God off the hook as God is not, even academically, guilty of any calamity we may face in life (or, for that matter, any incident of good fortune we may experience). Fourthly, and this I find the most exciting, it introduces jeopardy into God's economy. If God cannot see into the future, because the future does not exist, then God did not know that Jesus would go through with the sacrifice that would save humankind and God did not know that Jesus would successfully be raised from the dead. There is a possibility that God can lose a "battle."
I do not worship God because of what God can do but because of what God has done. That God took such a massive risk to save humankind makes God far more worthy of thanks and praise than if God just did a mundane thing without there being any potential cost involved.
Thanks be to the God of the possible!