Dan Drezner points out that resurgent worries about the dollar's decline are mostly ridiculous, which they are. As long as our trade deficit remains large, the dollar is going to tend to slide in order to match inflows to outgoes. Moreover, the dollar has been propped up over the last year by a global "flight to quality", aka US treasury debt. We should be glad that the dollar is declining, not merely because it makes our exports more competitive, but because it represents a restoration of confidence in the global economy.*
Nor, as Dan notes, are we particularly likely to lose our status as the world's reserve currency, because the Euro isn't very good at being a reserve currency for a number of reasons, and most of the other currencies have too small an economic base to sustain those kinds of capital flows. To which I'd add that the joys of being the reserve currency are somewhat overmagnified in peoples' minds--it's valuable, to be sure, but if the day comes when we lost that status, the sun will continue to shine, the US will continue to be the world's biggest superpower, and consumer electronics will still be available at attractive prices from developing world manufacturers.
But I must depart from Dan's theory of why people are getting obsessed with the dollar:
So, what's really going on here with the dollar obsession? I suspect that with the Dow Jones going back over 10,000, Republicans are looking for some other Very Simple Metric that shows Obama Stinks. The dollar looks like it's going to be declining for a while, so why not that? Never mind that the dollar was even weaker during the George W. Bush era -- they want people to focus on the here and now.
Believe me, people were obsessed with the dollar during the Bush era, too. Obsession with the value of the currency seems to be baked into the DNA of the right for some reason. If it's not the sliding dollar, it's gold buggery or petrodollars.