I don't think it's very important to achieve oil independence, just like I don't think it's important to achieve iPhone independence, or banana independence, or auto independence. For whatever reason(s) energy seems to make most rational people lose their perspective. If we are oil independent, and the Middle East blows up, oil prices will go up, so I don't see how our "dangerous dependence on foreign oil" really matters. The market is interconnected, as you can see by the chart of trade movements below.
Turns out, we have a rather diverse supply of oil. The following two graphs are from the BP Statistical Review of World Energy June 2014. The first, in tabular form shows where we get our oil imports. The second shows the same in pictorial form.
Keep in mind we produce a little over half of what we consume, the rest is from imports. So when you see the Middle East providing 20% of our imports, that's about 10% of our consumption. Canada is the biggest source of imported oil, and has been for some time. Mexico and Venezuela combined, are the next major source of supply, then the Middle East, combined.
By the way, in 2013 the world's largest producer of oil was Saudi Arabia at 11.5 million barrels per day (542.3 million tonnes), followed by Russia 10.8 million (531 million tonnes) and the US 10.0 million (446 million tonnes).
Production from the US this year will be about 11.4 million barrels per day and 12.6 million in 2015, at least according to the Energy Information Administration, which is part of the Department of Energy. Russian production has been growing modestly, and Saudi Arabian production is flattish over the past couple of year. If those trends hold the US will be the world's largest producer of oil, by a large margin. Compare this to 2003, when the US produced 7.4 million barrels per day. It's an amazing difference and all due to hydraulic fracturing. Also happens to be good for those concerned about carbon. More oil and more gas, means less coal means less carbon.