In the seventh chapter of Hebrews, the Levitical priesthood of the Israelites under the old covenant is compared to the priesthood of Christ, the great high priest of the new covenant. He said, under the old covenant, there were necessarily many priests because they were mortal and needed to offer sacrifices over and over, first for their own sins, then for the sins of the people. But Jesus, as our great high priest, needed only to offer himself once as the supreme sacrifice for man's sins: that he lives eternally and has an unchangeable priesthood. Wherefore he is able to save us to the uttermost if we come to God through faith in him, seeing he ever liveth to make intercession for us. He not only atoned for our sins by shedding his blood on Calvary's cross, he not only assures us of a resurrection unto eternal life, he saves us from the uttermost temptations, having faced and overcome all temptations common to man. It is difficult for me to imagine Jesus being tempted to sin, yet Hebrews 4:15, 16 says, "For we have not a high priest that cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin. Let therefore come boldly unto the throne of grace, that we may obtain mercy, and find grace in time of need."
He saves us from the uttermost point of despair-times when we lose hope and cannot see how things can possibly work out for us. But, if we cast ourself at his feet, he will sustain us until things do work out for us. Maybe not in the way we wanted them to but often better than we had hoped for. I have experienced this.
He save us to the uttermost from wrongful habits such as losing our temper, criticizing others, harmful eating and drinking and, one of the worst, gossiping: but only if we want to give them up.
He can save us from our sinful self-if we harbor hate, envy, jealousy, ill feelings, mistrust of other's motives, selfishness and impure thoughts and desires: but only if we seek his help.
Our problem is not Jesus' power to save us to the uttermost but whether we want to be saved to that extent.