After agreeing in January to allow rates on top income earners to return to higher levels of the 1990s, Republican leaders say they oppose any further tax increases or other measures to raise more tax revenue.
Meanwhile, Carney told reporters to expect Obama to release his budget proposal during the week of April 8, which GOP critics quickly noted would be well after the House and Senate versions came out.
"This is the first time in 90 years that the president's budget will actually come up after both the House and Senate have voted," McConnell said. "I hope that's not a reflection of a lack of seriousness but it is beyond, beyond tardy."
By clearly staking out positions in the formal budgeting process, Obama and Congress appear intent on trying to avoid the crisis-driven brinksmanship of the past four years that deepened Washington's defining political divide.
However, the familiarly partisan nature of Ryan's plan unveiled Tuesday and the Democratic response raised doubts of any lessening of that divide, which the public blames for legislative dysfunction.
A CBS News poll last week showed more than 70% of respondents want both sides to compromise to end the impasse over taxes and spending that dominated Obama's first term.
During the past four years, House Republicans passed 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 Democratic-led Senate was expected to take up its own version as soon as Tuesday.
Congress also must authorize an increase in the federal borrowing limit this summer.
Obama still calls for a comprehensive deficit-reduction package that would overhaul the tax system, cut spending and reform popular entitlement programs.
He and fellow Democrats insist that such an approach, labeled the grand bargain, must include increased tax revenue from wealthy Americans to prevent the burden of austerity steps in spending and entitlement reforms from hitting the middle class, the elderly and other vulnerable demographics too hard.
"My goal is not to chase a balanced budget just for the sake of balance," Obama said in the ABC interview. "My goal is how do we grow the economy, put people back to work, and if we do that we are going to be bringing in more revenue."
"If we control spending and we have a smart entitlement package, then potentially what you have is balance --- but it is not balance on the backs of the poor, the elderly, students who need student loans, families that have disabled kids. That is not the right way to balance our budget," he added.
Republicans led by their conservative base seek to shrink the size and cost of government, opposing any new tax revenue while pushing for spending cuts and lower tax rates that they say will spur more economic growth.
A comprehensive deficit-reduction deal appeared close during Obama's first term, but eventually fell apart over the deep ideological differences regarding taxes.
Such an agreement would reform the tax system to lower both personal and corporate rates while eliminating some loopholes and breaks. It also would reform Medicare and Medicaid and possibly Social Security to ensure their solvency.
The major sticking point of a comprehensive agreement will be taxes.
Obama and Democrats want to eliminate tax breaks and loopholes worth about $600 billion over 10 years as part of a broader $1.2 trillion deficit-reduction package that would include entitlement reforms.
Some Republicans have indicated support for ending such tax breaks as part of a broad deal. However, the fiscal-cliff agreement in January that resulted in higher tax rates on top income earners galvanized opposition by GOP leaders to further increases in tax revenue.
A sticking point in a possible compromise on taxes would be whether increased revenue realized through reforms, such as eliminating existing loopholes, go toward holding down rates or reducing the deficit.
Meanwhile, Republicans say Obama and Democrats must deliver on significant entitlement reforms.
"Democrats cannot be trusted to help fix our country's fiscal mess, if they cannot be trusted to balance the budget and create jobs," said a news release on Tuesday from the National Republican Congressional Committee. "The choice is clear: Democrats' perpetual deficits or Republicans' plan to balance the budget and spur economic growth."