Whether political theater or sincere outreach, President Barack Obama's so-called charm offensive is part of what shapes up to be the first formal congressional budget debate since he took office four years ago.

Obama invited a dozen Senate Republicans to dinner and then hosted lunch at the White House with two House leaders last week. He will meet separately in coming days with House Republicans and Democrats as both parties begin unveiling their budget plans for the rest of this year and 2014.

Wary Republicans call the president's new outreach a good first step, but said the style must be matched by substance.

"I believe anytime both parties are talking it's a good thing," Rep. Kevin McCarthy of California told CNN on Sunday, adding: "Is this about politics, or is this genuine? Only time will tell."

House Budget Committee Chairman Paul Ryan of Wisconsin also said Sunday on Fox that Obama must change from the campaigner-in-chief who Republicans believe is only interested in promoting party goals.

"Will he resume attacking Republicans and impugning our motives? Will he resume what is long believed to be a plan to win the 2014 elections?" asked Ryan, the GOP vice-presidential nominee last year who took part in last week's White House lunch with the president.

"Or will he sincerely change and try and find common ground, try and work with Republicans to get something done? That's what we hope happens," he added.

To Rep. Debbie Wasserman Schultz of Florida, the chairwoman of the Democratic National Conference, rebuilding damaged relations is necessary on both sides for any progress to occur.

"There is a trust deficit and the way in my experience in 20 years as a legislator that you close that trust gap is to sit down and continue to talk," she told ABC on Sunday. "I'm a lot more likely to reach consensus and agree on the facts when I have spent some time getting to know, and working with, the other side."

The Republican-led House has passed a proposal to fund the government through September -- the end of the current fiscal year -- and Ryan will unveil his 2014 spending plan this week to kick off the congressional back-and-forth.

Meanwhile, Senate Democrats plan to detail their own proposals as soon as this week, and the White House was expected to bring out its budget plan next month.

"The president will outline again through the budget process his priorities -- economic priorities and policy priorities, both in deficit reduction and in economic growth and job creation," White House spokesman Jay Carney told reporters on Monday. "And his budget will contribute to the process of regular order that we hope will produce bipartisan, balanced deficit reduction."

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.

During Obama's first term, 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 the funding measure for the rest of 2013, which is called a continuing resolution. It must pass by March 27 to prevent a partial government shutdown.

Congress also must authorize an increase in the federal borrowing limit this summer.

Here are possible outcomes:

The Grand Bargain

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.

Republicans, especially conservatives, oppose any kind of increase in tax rates or revenue in their push to reduce the size of government. They also want to shrink the costs of entitlement programs that are the main drivers of chronic federal deficits and debt.

Democrats want to preserve the social safety net of entitlements for the elderly, poor and disabled, with Obama and party leaders insisting on more tax revenue as part of any deficit deal.

In winning re-election last year, Obama campaigned on protecting middle class Americans from the burden of deficit reduction, calling for the wealthy to contribute more in the form of increased tax revenue and other steps as part of entitlement reforms.