Senate leaders had wanted to vote on the debt ceiling plan no later than Wednesday, before the arrival of the storm. It was unclear if Cruz's threatened filibuster would prevent an immediate vote from taking place.
If Congress doesn't pass a debt ceiling measure Wednesday, further action was unlikely until February 25 -- two days before the Treasury chief's deadline -- because of a shortened congressional work schedule in coming weeks due in part to the Presidents Day break.
Republicans across the ideological spectrum agree that another round of political brinksmanship could harm their party after it got blamed for October's federal government shutdown.
A recent CNN/ORC International poll found that 54% of respondents would blame congressional Republicans for a failure to raise the debt ceiling, while 29% would blame Obama and 12% would blame both.