Mr. Kight and other unemployed workers said they were incensed to learn they were living in one of a handful of states  many of them among the poorest in the nation  that might not provide the expanded benefits.

“It just seems unreasonable,” Mr. Kight said, “that when people probably need the help the most, that because of partisan activity, or partisan feelings, against the current new administration, that Perry is willing to sacrifice the lives of so many Texans that have been out of work in the last year.”

He was referring to Gov. Rick Perry of Texas, who has said he may decline the extra money rather than change state policy.

“I remain opposed to using these funds to expand existing government programs, burdening the state with ongoing expenditures long after the funding has dried up,” Mr. Perry wrote in a letter to Mr. Obama last week.

The governors contend that once the federal money ran out, they would have to continue providing the new benefits, which they say would force them to raise taxes on businesses. The federal money will end in two or three years in some states, or much later in others, depending on the size of the state allocation.

Image On Wednesday, Gov. Phil Bredesen of Tennessee became the first Democratic governor to express reservations on the issue. Credit... Mark Humphrey/Associated Press

Proponents say that nothing would prevent states from changing the laws back at that time.

The anger at the governors’ positions goes beyond just the unemployed workers who could directly benefit from the changes. Because eligibility rules for unemployment insurance are complicated and vary by state, many unemployed people do not even know whether they would be affected.