MIAMI  The federal government is showering households with tax rebates to spur spending and invigorate a troubled economy. But many Americans are so consumed with debt and the soaring price of gasoline that they are opting to save the money or use it to pay bills, according to surveys, sales data and interviews with people from Florida to California.

Between late April and the end of last week, the Treasury handed out more than $50 billion of the $100 billion in tax rebates it plans to distribute to 132 million households. But only once in the last six weeks have chain stores registered an increase in sales, according to the International Council of Shopping Centers, whose weekly sales survey is a widely watched barometer.

“The initial sense is that people are not running out to the malls to spend their checks,” said Stuart G. Hoffman, chief economist at the PNC Financial Services Group in Pittsburgh. “It’s not quite proving to be a hot potato that’s burning a hole in people’s pockets.”

Here in Miami, where the economy remains stuck in the orbit of plummeting real estate prices, Guillermo Gonzalez is one of those using their tax rebates to dig out of debt.