Our spirit is not our problem. The born-again Christian receives a new spirit at conversion, that is just like Jesus' (1 John 4:17) because it is the Spirit of Jesus. Our born-again spirit is always willing to do God's will. It's our flesh that is the problem.

The flesh, as Jesus describes it, not only includes our physical body but also describes our soul. God has given every believer everything it takes to walk in victory, but "we have this treasure in earthen vessels" (2 Corinthians 4:7). That is saying that our spirit, where God has deposited all of His power and glory, is inside our flesh.

That doesn't mean we cannot tap into this divine source. As much as we renew our minds and act on the Word of God, we can experience the divine flow through our physical bodies. 

Just as we must use our muscles to increase in strength, we must exercise ourselves (soul, mind and body) unto godliness (1 Timothy 4:7-8).

Prayer is one important way of exercising ourselves unto godliness, and is why Jesus admonishes us to watch and pray.