Today's Washington Post / ABC News poll had much stronger numbers for Barack Obama than other polls we've seen over the past week, but even so Mitt Romney has one key area of residual strength—the budget deficit.
In my view that's probably right, Romney is the better candidate on the deficit. But the framing of this question in the press is extremely misguided, and being "better" on the deficit is generally taken to mean that he would produce a smaller budget deficit. The overwhelming preponderous of the evidence indicates that's mistaken. When Republicans are in the White House they tend to be vigorous advocates for more borrowing, and Democrats are weak proponents of deficit reduction. During the Bush years, 12 Democratic Senators joined the GOP to pass the Bush tax cuts. The enormous deficits of the early Ronald Reagan years would have been impossible without the complicity of a large bloc of "Boll Weevil" conservative House Democrats. And when Bush was in office, Democrats and Republicans would sometimes even come together across party lines to create big new deficit-financed increases in domestic spending. When Democrats are in the White House, they're much more vigilant about deficits than they are when Republicans are running the show and the GOP transforms from being the crazy borrowing party to the maniacal fiscal scold party.
You should certainly expect a Romney administration to squeeze domestic spending, particularly on the poor, but all indications are that Romney's cuts won't come close to paying for his tax cuts and defense spending hikes and congress will be much more inclined to endorse big borrowing if Romney's in the White House. A second Obama administration, by contrast, will lead to smaller deficits—the only real question is how much smaller.
But this is precisely why if the only thing you care about in the election is the size of the federal budget deficit you should almost certainly vote for Mitt Romney. A smaller deficit will do nothing to help the economy right now. A bigger deficit would be at worst a minor waste of money on low-value projects (stockpiling extra tanks or whatnot) and at best a meaningful way of reducing unemployment and preserving the country's stock of physical and human capital.