Though such figures are modest, they are actually up from earlier expectations, and have translated into improving consumer sentiment and spending. According to IMF predictions, all three of Europe's top economies – France, Germany, and Britain – will see growth. France is expected to see token improvement in 2013 and 2014; Germany should grow 0.5 percent this year; and the British economy is forecast to grow 1.4 percent in 2013 and 1.9 percent in 2014.
But that would certainly change if House Republicans and the White House fail to reach an agreement by Oct. 17 on raising the debt ceiling, and the US Treasury becomes unable to raise more cash.
The European economy is inherently exposed to effects from across the Atlantic, because is financial sector and that of the US are closely intertwined. "The US is Europe's second biggest trading partner," says Mr. Wall, and "there is a strong degree of correlation with US financial sector."
But additionally, a US default would strike at the engine of the European recovery: European exports to the US. A weakened US dollar makes European exports more expensive, undermining the region's competitiveness, just as year of painful adjustments are starting to pay off.
(Read more: Market has it right on default risk: Ex-JPM banker)
"If it comes to a default, however unlikely, for sure the recovery would be at stake. It would be such a huge shock that European risk premiums would rise again massively," says Matteo Cominetta, a London-based European economist with HSBC.
The effects in southern Europe – Spain, Italy, Greece, and Portugal – could be worse, as its economic recovery is underway at a much slower pace than northern Europe.
The two giants of the periphery, Spain and Italy, are gaining traction, although both remain in a precarious position due to political uncertainty and unpopular governments.
Analysts say that Spain in particular is showing signs of recovering from the southern economic malaise. Its leading stock index, the IBEX 35, is up more than 50 percent in the past 14 months. Since mid-September, lenders have been demanding a higher premium to hold Italian 10-year bonds than Spanish ones.