WASHINGTON — The Senate on Monday agreed to consider a temporary extension of unemployment benefits after four Republicans joined Democrats in voting to debate the proposal, which has become the focus of an intensifying fight over deficit spending.

Despite objections from conservative Republicans, the Senate voted 60 to 34 to move ahead with a measure that would keep checks flowing to jobless Americans who are exhausting their benefits and maintain federal subsidies for health insurance for the unemployed. The measure must clear other procedural hurdles, but Democrats hope to win its approval this week.

The $9 billion cost of the aid would be added to the deficit, which Democrats said was justified because of the grim national employment picture.

“Let us help the families who are struggling in this difficult economic time,” said Senator Max Baucus, Democrat of Montana and chairman of the Finance Committee, who said the infusion of federal aid would help the overall economy recover.