Democrats and Republicans disagree on whether the nation's richest families should receive the cuts.
The president and most Democrats want them extended to any couple earning $250,000 or less, but Republicans want to make them permanent for everyone.
Also on the agenda is a controversial bill that would end "don't ask, don't tell." So far, Senate Republicans have blocked that bill.
The Senate is also expected to pass a food safety bill this week, giving the Food and Drug Administration authority to recall tainted products and require food manufacturers to follow stricter safety standards.