The $838 billion economic bill survived a key test vote in the Senate Monday, setting up a final vote Tuesday. The plan must then be reconciled with an $819 billion version from the House of Representatives.
After Wall Street closed Monday, President Barack Obama pressed his case for the stimulus plan, warning that failing to act swiftly and boldly "could turn a crisis into a catastrophe."
"The big story for financial markets remains the progress of the U.S. bailout package through the Senate later," said James Hughes, market analyst at CMC Markets.
The FTSE 100 index of leading British shares dropped 56.02 points, or 1.3 percent, to 4,251.59, while Germany's DAX fell 82.84 points, or 1.8 percent, at 4,583.98. The CAC-40 index in France was 51.17 points, or 1.6 percent, lower at 3,083.70.
Earlier in Asia, Japan's Nikkei 225 stock average fell 23.09 points, or 0.3 percent, to 7,945.94, while Hong Kong's Hang Seng closed up 0.8 percent at 13,880.64 after swinging in and out of negative territory throughout the session.