Majority Leader Harry Reid said "we know it would pass." He urged House Speaker John Boehner to return to the negotiating table with Obama.
Reid's remarks came the day after House Republicans failed to pass a "Plan B" measure to raise taxes on million-dollar-plus incomes.
Senate GOP Leader Mitch McConnell countered with an offer to vote on prior House legislation extending all Bush-era tax rates.
McConnell said that if Democrats have a plan that can win a filibuster-proof 60 votes in the Senate then "let's vote."