With the crisis in Europe still raging, analysts are frantically trying to game out what a euro zone implosion would mean for the United States. Yesterday, the Federal Reserve Bank of San Francisco put out a research note pegging the odds of a U.S. economic contraction in early 2012 at “greater than 50%,” noting that a European sovereign debt default (Greece, say) would very likely plunge us into recession.

Part of the reason for that is that Europe is one of our major trading partners — accounting for about one-fifth of U.S. exports. Over at Real Time Economics, Josh Mitchell put together a handy chart, using Wells Fargo data, showing which states export the most goods to Europe, and hence would get hit hardest by a Europe slump:

Utah’s gold exports, South Carolina’s auto exports, and West Virginia’s coal exports are potentially at greatest risk. The one sliver of good news is that, as Wells Fargo notes, most states have major trade flows primarily with countries like the United Kingdom, France, the Netherlands and Germany, rather than the most fragile countries like Greece and Italy and Spain. So it’s tough to say, exactly, how a slowdown overseas would play out here.

Meanwhile, the bigger, scarier unknown is whether financial mayhem in Europe could wreak havoc on U.S. banks. Reuters reports that the newly created Financial Stability Oversight Council is desperately trying to figure out which firms are exposed to a euro zone crisis. Indirect U.S. bank exposure to Europe could total more than $4 trillion, although it’s unclear how much of those potential losses would be limited by hedging and so forth. That $4 trillion is a worst-case scenario.

Even so, it’s a large enough number that policymakers are racing to build up a firewall. The Federal Reserve will reportedly initiate a new round of stress tests for U.S. banks soon, and Brad DeLong says the word from Washington policymakers is that they are “pressing leveraged banks to reduce their exposure to euro risk by selling their risky European government bonds off to other private-sector investors.” Still, given the large sums of money involved, it’s not surprising that analysts at the San Francisco Fed and elsewhere are jittery.