WASHINGTON — Hillary Rodham Clinton’s split with President Barack Obama over a foreign policy “organizing principle” isn’t likely to be the last time differences emerge between the two. How she handles those breaks could be among her biggest challenges to a successful run for president in 2016.

While Obama and Clinton share similar views in many areas, the former first lady’s interview with The Atlantic offered her most significant break with her onetime campaign rival.

She said Obama’s “failure” to back the rebels in Syria led to the rise of Islamic State militants in Iraq. She appeared dismissive of Obama’s approach to foreign policy, saying “’Don’t do stupid stuff’ is not an organizing principle.”

Clinton will likely seek some separation from Obama if she runs for president — especially if Obama’s approval ratings stay near 40 percent. But decoupling from a two-term president of your own party can be tricky.

Republican Sen. John McCain was weighed down by President George W. Bush’s poor approval ratings in 2008 and Democrats’ contention that electing McCain was tantamount to a third Bush term. In 2000, many Democrats urged Vice President Al Gore to campaign more emphatically on President Bill Clinton’s economic success instead of distancing himself from the Monica Lewinsky scandal.

A few areas where Obama and Clinton’s views will be closely watched as 2016 approaches:

Foreign policy

How Obama handles a series of foreign crises — Iraq, Gaza, Ukraine and Syria — could directly influence a future Clinton campaign.

The president’s decision to launch airstrikes in Iraq comes only two years after he campaigned for re-election on a record that included ending the Iraq war.

In her book “Hard Choices,” Clinton wrote that she “came to deeply regret” her vote to authorize the war, a decision that Obama used as a foil in the 2008 campaign. Clinton has not yet commented publicly on Obama’s latest moves in Iraq.

The book includes instances in which she and Obama shared divergent views. In Egypt, she wrote that she was concerned about the U.S. being seen as pushing out a long-term partner in Hosni Mubarak without a clear picture of the region’s future.

But Republicans say Clinton will be hard-pressed to draw such distinctions, since she was an integral member of his team as secretary of State.

“It’s certainly hard to see how she doesn’t own the foreign policy record of this administration,” said GOP strategist Ralph Reed.

Economy

Clinton often talks about the challenges faced by many Americans who haven’t benefited from the economic recovery. Obama has presided over steady job growth during the past six months but it remains to be seen whether Clinton could run on an economic comeback story.

In a July interview with the German magazine Der Spiegel, Clinton said the research of economist Thomas Piketty showed that income inequality is “threatening to democracy.”

“Even during the Great Depression people in the streets believed that they could make it and they would be better off. Now the relative wealth is much higher, but the disparity makes people believe that they’re stuck,” said Clinton, who has pointed to her husband’s economic record as a model.

Immigration

Clinton has kept a close line with Obama on immigration — both on the need for a comprehensive overhaul and the influx of unaccompanied minors from Central America across the U.S.-Mexican border.

Clinton said last month she supported creating a refugee screening process for the children in their home countries to discourage the dangerous journeys to the U.S., an approach that is similar to a pilot program under consideration by the White House.

Obama is expected to announce executive actions to address immigration, which could include a plan to give work permits to millions of immigrants living in the country illegally.

Climate change

Clinton told college students in March she hopes for a “mass movement” on climate change, signaling the issue could figure prominently in a campaign.

Obama plans to attend a United Nations summit on climate change next month and speak at the Clinton Global Initiative meeting, where one session is titled “Confronting Climate Change is Good Economics.”

Environmentalists are awaiting a decision by Obama on the Keystone XL pipeline, which would carry oil in western Canada to refineries on the Gulf Coast. Environmentalists oppose the pipeline, and Obama has said he would allow it to be built only if it doesn’t exacerbate carbon pollution.

Clinton has avoided directly commenting on the project, citing the ongoing review.