My best advice would be to pray that you would do good work, and that God would use your gifts and abilities in some clear way. You are right that there are more PhDs than there are tenure track jobs. But for some disciplines, there are other options — government, industry, and non-profit sector work.
Don't give up on getting a tenure track job, but keep the main goal — being gainfully employed and using your gifts — as the centerpiece.
If you are interested in small Christian schools, the job market may be better there. Your options are better too if you are open to moving.
But, overarching this all, stick with positive friends. Don't get sucked into a cycle of worry. What you are doing should be worthwhile for its own reasons.
Let's take a step or two back and assess your situation. You're a few years from graduating. As you see within your program, students begin to get restless and pessimistic, too far from the start to be excited but not close enough to the end to be happy. At this point in their programs, bad attitudes abound as students realize they are not as ready for their desired jobs as they could be. Furthermore, looking at the immensity of the dissertation and the required research still needed to complete your degree can lead to the anxiety you describe. Thinking too much about these worries can in turn distract from the focus you need to take the everyday small steps that will get you to the finish line.
From a practical perspective, continue to do everything you can to ensure your CV is well-padded: teaching, research excellence, conference attendance, networking, online social networking, and any other professionally-oriented activities that might give you an edge in your field. If you have a good relationship with your thesis advisor, request a meeting where you can discuss your roadmap to graduation and how best to position yourself for the career you desire. If you are in a discipline where a postdoctoral stint is common or required, you can begin to generally think about what research areas you would be interested in pursuing. Be aware that even if your publication record is modest heading into a postdoc, you still may be able to aim high institution-wise if you search for newer assistant professors to serve as your project advisor.
From a faith perspective and desiring to put panic aside, I have a few suggestions. I tend to be a worrywart myself and have always had anxiety about my academic performance. As an undergraduate who regularly poured her heart out to God about my academic stresses and worries, I received an anonymous note one day that simply contained a decorated rendering of Philippians 4:6 (NLT): "Do not worry about anything; instead, pray about everything. Tell God what you need, and thank him for what he has done." This is of course good advice. The helpful thing to me about this passage was not only the counsel to stop worrying and exchange the worry for pouring out my anxieties to God, but also the understanding that I could reflect on his faithfulness to me throughout the years and give him words of gratitude for guiding me and blessing me. Somehow listing off ways that God has blessed me, big and small, and communicating those, helps to put my heart at ease as I realize that he is always there in my life. It's been almost 14 years since that note graced my dorm mailbox, and I still think back to it when I descend into worry.
There is a second Scripture that has been helping me lately as I am nearing the end of my own stint as a postdoc and looking towards my next career steps. Trusted friends have often urged me to have faith that God will lead my husband and me to our next positions in life. Having faith that things will turn out amidst uncertainty is always difficult.
I recently heard a sermon on the definition of faith found in Hebrews 11. This chapter starts out with the assertion that "Faith is the confidence that what we hope for will actually happen; it gives us assurance about things we cannot see." As an academic, I had always approached this passage in a rather sterile and heady sense: that faith was something that was swimming around in my brain and that I should have an intellectual awareness that through faith God would give me the confidence that things would go well in the future. However, the recent sermon challenged listeners to look at the rest of the chapter, where example after example of faith is given. In each case it is said that "by faith" each of these people took an action in response to God — not necessarily knowing the outcome. This infers that faith is not simply just an awareness of God's follow-through; it calls us to act as we follow God’s call, with faith in his purposes.
I don't want to give the impression that God will answer all dreams the way we think we desire them. In my own life I definitely am not doing what I’d dreamed of doing after my PhD (I thought I'd instantly go into teaching at a small Christian liberal arts college), but I definitely do see God's hand in leading me here and am at peace with the path he's led me on. Same with my time in grad school. I did not expect it to go the way it did (it was a very difficult, challenging time), but reflecting on it I am glad I followed his call to persevere, and I can see many ways he deepened my relationship with him during the time there.
I would encourage you, in these final years of your program, to do the work that you believe you have been called to and have faith that you will find a fulfilling path after school.