Right now about 640,000 jobless Americans are receiving this last tier of benefits, according to the National Employment Law Project. The money, appropriated in the 2009 federal stimulus package, was initially intended for states with jobless rates higher than they were two years earlier. Since the recovery has been much slower than predicted, though, Congress decided last December to allow states to continue receiving the money if their unemployment rates were higher than they were three years earlier. States simply needed to change “two” to “three” in the relevant state law.

Some economists say that cutting off the long-term unemployed from extended federal assistance could backfire by putting further strain on state economies instead. Indeed, most states were quick to make the one-word change, counting on the federal money not only to support ailing families but also to serve as a strong stimulus (jobless benefits are normally spent more quickly than, say, tax refunds). Nearly every state — Arizona included — had opted into the extended benefits program when it was introduced.

But now Arizona is reluctant. When Gov. Jan Brewer called a special session to address the issue last week, legislators didn’t introduce a bill. Republican legislators said they would consider the change only if it were packaged with other provisions, including tax cuts and stricter rules for receiving unemployment benefits in the first place.

“We prefer to look for long-term solutions so when the Obama administration money runs out Arizonans will have jobs,” said Andy Tobin, the Republican speaker of the house.

Some Arizona lawmakers expressed discomfort with the prospect of accepting more federal money.

“This is not free money,” said Al Melvin, a Republican state senator representing Tucson. “This is America’s money. We have a $14 trillion debt that has to be paid, and we need to stop spending money we don’t have.”