WASHINGTON (Reuters) - Barely a week in office, Barack Obama is already embroiled in the first major political challenge of his fledgling presidency -- trying to persuade Republicans to back his $825 billion economic stimulus plan.

President Barack Obama speaks about climate change reform before signing executive orders in the East Room of the White House in Washington, January 26, 2009. REUTERS/Jason Reed

Obama has big Democratic majorities in the House of Representatives and the Senate, lawmakers who are likely to settle their differences with Obama over the plan and support it.

So why is he bothering with Republicans at all?

One reason is a simple case of math. Democrats lack a sufficient majority in the Senate to stop Republicans from engaging in vote-delaying filibuster tactics.

But more importantly, Obama needs the political cover that having some Republican support would bring for an unproven plan that will add to America’s budget deficit and may or may not stop the U.S. economy from its downward slide.

“Republicans offer him a degree of credibility,” said Democratic strategist Doug Schoen, who worked in the Clinton White House.

Obama has been hearing out Republicans on their concerns. He is to visit Capitol Hill to meet Republicans on Tuesday.

He spoke to Republican congressional leaders on Friday at the White House and urged them to think beyond their conservative base of support, as exemplified by talk radio host Rush Limbaugh.

“You can’t just listen to Rush Limbaugh and get things done,” Obama said, according to those familiar with the conversation.

He also reminded them of the political clout he gained by his solid election victory over Republican John McCain on November 4.

“I won,” he said, in what White House press secretary Robert Gibbs described as a lighthearted moment that prompted laughter in the room.

WALKING A TIGHTROPE

When Republicans look at his plan, they see a lot of pork-barrel spending that does not seem aimed at creating jobs but rather directed at taking care of traditionally Democratic constituencies, such ass $16 billion in grants for college students.

They worry that it would take too long to get a lot of the stimulus money into the pipeline, and they would like to see more in the way of tax cuts. Currently the $825 billion package includes $275 billion in tax breaks.

McCain, who has been wooed by Obama as a possible ally in the Republican minority, says he would vote against the plan as it stands now.

“I think there has to be major rewrites if we want to stimulate the economy,” Arizona Sen. McCain told “Fox News Sunday.”

Some Republicans face the challenge of trying to stare down a popular new president who wants to do whatever it takes to save the economy from collapse.

Experts say Republicans are walking a tightrope.

“The American people, almost 80 percent of whom approve of his presidency right now, I think will not look kindly at anything they see as partisan obstructionism,” said Norman Ornstein, a political expert at the American Enterprise Institute.

In normal times, Republicans would be on sound political footing rejecting the kind of spending that the package entails. Some experts are not sure they can stick to business as usual in an emergency climate, however.

“Republicans can’t forsake their fundamental principles,” said Republican pollster Whit Ayres. “But the country wants Republicans and Democrats to work together to address what is becoming every day a more serious crisis.”

Maine Republican Sen. Susan Collins, who typically adopts a moderate position, told MSNBC she had a lot of questions about the stimulus because it includes items that are worthwhile but “I’m not sure they meet the test.”

Republican strategist Scott Reed said he believed Republican lawmakers are on safe ground questioning the scope of the package.

“I think Republicans are very effectively bringing up the level of the spending and the effectiveness of it,” he said.