With one budget fight behind him, President Barack Obama will offer a long-term plan for deficit reduction this week in preparation for bigger U.S. spending battles ahead, the White House said on Sunday.

Senior White House adviser David Plouffe said Obama would explore savings in defense spending and the popular Medicare and Medicaid health programs for the elderly and poor as he seeks ways to reduce the $1.4 trillion annual deficit.

White House officials said Obama would release his plan on Wednesday.

Plouffe and Republican leaders who control the House of Representatives said the difficult 11th-hour spending deal to avert a government shutdown on Friday was the first major test of the new era of divided government.

Much harder battles lie ahead over the budget for the 2012 fiscal year that begins in October, and over the need to raise the current $14.3 trillion limit on U.S. government borrowing authority in the next few months.

We're going to have tough disagreements. It's going to be hard to bridge divides, Plouffe said on NBC's Meet the Press, adding the budget deal showed compromise was still possible in Washington.

Representative Paul Ryan, who authored a Republican 2012 budget plan last week as head of the House Budget Committee, said he expected a political fight over the debt ceiling.

There will be some kind of negotiations and yes it probably will go up to some sort of a deadline, he said on Meet the Press, adding: Our strategy is not to default. Our strategy is to get spending under control.

Obama's Democrats and opposition Republicans agreed late on Friday to cut $38 billion in spending for the last six months of this fiscal year.

It was the first big test for both sides since Republicans took control of the House in November's elections on promises to rein in government and cut federal spending.

The deal, which still must be approved by Congress this week, prevented a shutdown that would have idled 800,000 federal workers, closed national parks and monuments and delayed paychecks for troops in Afghanistan and Iraq.

But lawmakers on both sides of the political divide were disappointed. Republican Representative Mike Pence, popular with fiscal conservative Tea Party activists, said on ABC's This Week the deal was probably not good enough.

Representative Chris Van Hollen, the top Democrat on the House Budget Committee, said he would reserve judgment until he sees more details but believed the deal would be able to pass Congress.

Obama, Republican House Speaker John Boehner and Democratic Senate leader Harry Reid hammered out the accord after weeks of bitter political wrangling that raised questions about Washington's ability to function under a divided government.

Plouffe said Obama, a Democrat, would not embrace Ryan's budget plan, which would save $6 trillion over the next decade, partly by cutting government-run health programs for the poor and elderly.

But he said Obama's plan would look for savings in the Medicare and Medicaid programs, and would explore ways to strengthen the Social Security retirement program and renew an effort to raise taxes for the wealthiest Americans.

You're going to have to look at Medicare and Medicaid and see what kind of savings you can get, Plouffe said on NBC.

In the process of sitting down and talking about our spending and our programs, if there can be a discussion about how to strengthen Social Security in the future, he's eager to have that discussion, he said.

Plouffe told CNN that seniors, the poor, and the middle class were being asked to bear most of the burden under Ryan's budget plan.

If you weren't giving enormous tax cuts to millionaires, you wouldn't have to do that, he said.

So the president has said and it is in his budget, for people making over $250,000, he would favor having the tax cuts eliminated for them.

(Additional reporter by Alister Bull and Dave Clark; Editing by Laura MacInnis)

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