Europe has a $1 trillion problem.

As difficult as the last two years have been for Europe, 2012 could be even tougher. Each week, countries will need to sell billions of dollars of bonds — a staggering $1 trillion in total — to replace existing debt and cover their current budget deficits.

At any point, should banks, pensions and other big investors balk, anxiety could course through the markets, making government officials feel like they are stuck in a scary financial remake of “Groundhog Day.”