Sixty senators voted to move ahead with debate on the $6.4 billion measure. That is the exact number required to move the bill forward.
The bill is a top priority for Democrats, but most Republicans object to it, arguing the spending needs to be offset with cuts elsewhere in the federal budget.
The plan would provide unemployment benefits for eligible workers for another three months.
More than a million jobless Americans lost their long-term unemployment benefits last month when Congress failed to renew them.
If the measure passes the Senate, it faces an uncertain future in the House.