A CBS News poll last week showed more than 70% of respondents want both sides to compromise to end the brinksmanship over taxes and spending that dominated Obama's first term.
During the past four years, House Republicans pushed through partisan budgets that Senate Democrats ignored, forcing the repeated extension of past spending plans.
Meanwhile, the president's budget proposals generated little support in Congress.
The upcoming negotiations are complicated by lingering fiscal issues from past showdowns.
Deep cuts to military and other discretionary spending took effect this month, and both sides were expected to try to soften their impact through a separate funding measure for the rest of the current fiscal year, which ends September 30.
Called a continuing resolution, it must pass by March 27 to prevent a partial government shutdown. The Republican-led House passed its version last week, and the Democrat-led Senate took up its own version this week.
Congress also must authorize an increase in the federal borrowing limit this summer, and Republicans have made clear they intend to leverage that moment to try to extract concessions.
A comprehensive deficit-reduction deal appeared close during Obama's first term, but eventually fell apart over taxes.