Potential Republican contenders for the White House face a tough strategic decision: How much to woo the Tea Party?

Some, like Sarah Palin, Donald Trump and Tim Pawlenty, appeared at Tea Party Tax Day events this weekend. Others, like Mitt Romney and Haley Barbour, are charting a more cautious course.

Potential candidates have increasingly courted Tea Party groups, the grassroots political force that seemingly helped propel Republicans into control of the House of Representatives in November.

But Washington is set to consider issues such as whether to overhaul Medicare and raise the debt ceiling, which some fear could hamper GOP unity. Republicans needed help from House Democrats to pass a government funding bill after 54 Republicans, many of them aligned with the Tea Party, voted to shut the government down instead.

That kind of position might help inspire primary voters in Iowa and New Hampshire early next year. But it could be more difficult to explain in the general election in November of 2012, where the election could be won or lost with less engaged independents.

Palin, a former Alaska governor who is most closely associated with the fiscally conservative, right-leaning group, railed against President Obama and his budget priorities at a Tax Day Tea Party rally in Madison, Wis., Saturday.

Pawlenty, a former Minnesota governor who is trying to expand his base, has aggressively attempted to tie himself to the group. He spoke at a Tea Party rally in Iowa Saturday to shore up support.

In another battleground state hundreds of miles away, business magnate Trump delivered a similarly fiery anti-Obama message to Tea Partiers.

The Tea Party has already emerged as a strong political force, even though many people have yet to announce formally their candidacy. Grassroots groups across the country have mobilized supporters to test out the candidates, while various national groups have organized presidential debates and political action committees to get into the game.

The Tea Party's influence "will be an important factor inside the Republican primary system," said Stephen Ansolabehere, a political scientist and professor at Harvard University.

Potential candidates such as Pawlenty are looking to the Tea Party to break out of the mold and expand their base outside of the Republican establishment.

Romney has consistently praised the Tea Party for bringing "hope that we can rein in our profligate federal government," he wrote in an op-ed in the Orlando Sentinel last week.

But the former Massachusetts governor and other potential candidates like Mississippi Gov. Barbour have adopted a more cautious approach than some of their counterparts.

Romney didn't make an appearance at any Tea Party Tax Day rallies this weekend. Barbour has also praised the Tea Party for injecting enthusiasm into the Republican party but has generally maintained a slight distance from the group.

Despite the movement's rapid surge in popularity, there is still concern that it may cause internal frictions within the party and alienate senior citizens with its goal to overhaul entitlement programs such as Medicare.

Tea Party Influence Questioned

Budget negotiations on Capitol Hill have already exposed some of the fray between the Republican leadership and the Tea Party-backed freshmen who were unwilling to cave in to Obama and Democrats' demands, even if it meant shutting down the government.

"The way the first round of negotiations worked out doesn't help the Tea Party much," Harvard's Ansolabehere said. "They were able to make strong political gains in terms of holding out in what they believe in, but it also allowed the Republican leadership to make a deal with moderate Democrats.

"So the next couple of budget negotiations will probably see the same coalition of moderate Democrats, and even some liberal Democrats ... getting together with Republicans to make deals. So the real extreme anti-budget, anti-government rhetoric has to be downplayed."

A recent analysis by Ansolabehere and Harvard professor James M. Snyder Jr. found that the Tea Party's influence in the 2010 mid-term election might have been exaggerated, and the movement performed as well as other groups within the Republican party, including Christian conservatives.

"While the large number of victories for Tea Party-backed candidates suggests electoral appeal and political clout, it seems that a Tea Party endorsement actually didn't matter all that much," the report states. "In an election year that favored Republican politicians because of the prolonged economic recession and stubbornly high unemployment, Republican politicians did about as well as one would expect."

Public views of the Tea Party have gotten more negative, according to a poll released this month by the Pew Research Center for the People and the Press. Of those polled, 29 percent said they disagreed with the Tea Party, nearly double the number at the same time last year, when more people agreed with the movement. A greater number of moderate Republicans disagree with the Tea Party today than a year ago, according to the survey.

Still, observers agree that the Tea Party, which has increasingly built more momentum and clout since it got off the ground two years ago, is expected to play a vital role in the upcoming election, although the degree to which it actually influences the outcome remains to be seen.