The reason for the current government shutdown is Republican opposition to, and Democratic support of, the Affordable Care Act, a.k.a. Obamacare. The majority of Republicans oppose Obamacare and are refusing to fund it. The bill funding Obamacare also contains provisions to keep the government operating.
Bible promises of faith healing are found all the way back in the Hebrew Bible/Old Testament. Many Christian churches, such as the First Century Gospel Church that has as faithful members Herbert and Catherine Schaible who were so strong in their Christian faith and belief in the Bible promises of faith healing that they let two of their children die, rely on Isaiah 53:5 which reads, "But he was pierced for our transgressions, he was crushed for our iniquities; the punishment that brought us peace was on him, and by his wounds we are healed." Christians believe this verse is referring to Jesus. (For a powerful and well documented essay which disputes New Testament claims to Old Testament prophecy by the American founder and Deist Thomas Paine, click here.)
The New Testament makes numerous promises to Christians regarding the ability to heal people through prayer and faith. For example, James 5:14-15 teaches, "Is any sick among you? let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord: And the prayer of faith shall save the sick, and the Lord shall raise him up; and if he have committed sins, they shall be forgiven him."
Another popular faith healing Bible promise is found at Mark 16:17-18 which has the dead and then resurrected Jesus promising that believing Christians will have healing powers. It claims that Jesus said that those who believe the gospels (the gospels were not yet written when it is claimed Jesus made this promise) "shall lay hands on the sick, and they shall recover."
This is a huge Bible promise straight from Jesus himself! Uncharacteristically for the Bible, it is not ambiguous. It has Jesus directly promising all male Christians ("He that believeth on me") the power to do all the thing that Jesus is said to have done, such as walking on water, turning water into wine, feeding thousands of people with only a very small amount of food and drink, making the blind see and the deaf hear and actually raising people from the dead. PLUS the power and ability to do even more than these amazing things! The only possible condition put on this promise is that male Christians won't have these powers and abilities until after Jesus dies, comes back to life and goes back up into heaven ("because I go unto my Father"). Based on the Bible and Christian teachings, this condition has already been satisfied and Jesus is already back in heaven with his father. So there is absolutely no reason for male Christians not to have these heavenly Christian powers at their disposal.
Armed with the Jesus-centric healing powers, any male Christian can right now go into any hospital and start clearing it out. In fact, they don't even have to GO into a hospital based on Jesus' promise to them in John 14:12-14. All they have to do is ask in prayer that all sick and injured people be immediately healed and Jesus will do it! However, it seems this Bible promise from Jesus is false. For example, US Senator and strong Christian and member of the religious right Ted Cruz has publicly prayed for fellow Christian Saeed Abedini (Cruz is pictured above praying in front of the White House on September 26, 2013) who is currently being held in prison in Iran to be released from prison. Abedini is as of this writing still in the Iranian prison. However, Obama has recently asked the Iranian government to release him, so he may be released because of Obama's request, not because of Jesus' empty promise or the prayers of Cruz to the Christian diety.
Another sign that the promises of faith healing in the Bible are false is the fact that children die every month in the US because they have sincere Christian parents who actually believe and act on these false promises.
Based on the poor track record of the Bible and its promises, don't expect an end to the need for health care or the imminent end to the government shutdown.