Without action by Congress, all Bush-era income tax cuts will expire at the end of the year.
The morning debate saw impassioned speeches from both sides of the aisle early on in the session.
The Democrats are already eyeing the 2010 elections and eager to depict Republicans as guardians of the rich with two proposals over Bush-era tax cuts.
"We think it's wrong for tax breaks to go to millionaires," said Sen. Chuck Schumer (D-New York). "We think it's correct that it goes to the middle class. That is going to be one of our watchwords, one of the things you will see us continuing to work on next year."
The Democrats' first proposal would have kept the cuts in effect except on incomes over $200,000 for individuals and $250,000 for couples.
The second propsal would have let taxes rise on incomes over $1 million. It appeared crafted to appeal to senators from states with large high-income populations.
However, both were shot down by Republicans, who want a plan that extends the cuts to those making more than $1 million. They argue not extending the cuts will hurt small businesses and slow down job creation.
On the other side, Democrats say those cuts will only benefit the rich.
Republicans dismissed the finger pointing as the last gasp of a Democratic Party that lost its majority in the House in midterm elections, surrendered several seats in the Senate and will be forced to share power beginning in January.
But the rhetoric subsided quickly after the votes, and Senate leaders in both parties said they hoped political clashes would give way to compromise in the next several days.
Among them are an extension of jobless benefits for the long-term unemployed and extension of additional expiring tax breaks for lower- and middle-income workers even if they don't make enough to owe the IRS money. College students would also benefit under the White House's proposals, as would companies that hire the unemployed.
Also part of the discussions is a possible increase in the federal debt limit, which allows the government to continue to borrow to meet its financial obligations.
The Associated Press Contributed to this report.