Theory one: President Barack Obama is a pushover, jerked around by his own party's liberals, House Speaker Nancy Pelosi and the Chinese.

Theory two: President Barack Obama is tough in a fight, as he's showing in frontal assaults on insurance companies, teachers unions and the Taliban.

President Obama might seem like a pushover with some liberals and the Chinese, but in other regards, he's showing he's tough by taking on insurance companies, teacher unions and Pakistan. Executive Washington Editor Jerry Seib explains.

This is a week in which those opposing theories are being put to the test. The epic health-care struggle heads into what promises to be, finally, the real stretch run, pushing the president deeper into what is not only the biggest fight of his career, but also a testing ground for how he acts under maximum pressure.

The trouble in generalizing on this question—tough or not?—is illustrative of the difficulty in trying to typecast a leader who remains in many ways an enigmatic figure more than a year into his presidency. Mr. Obama is an engaging public figure, yet can be cool and detached personally. He's broadly popular with voters, even as they downgrade their views of his job performance.

His ideology is nearly impossible to categorize. If Bill Clinton could be neatly characterized as a New Democrat, and George W. Bush as a compassionate conservative, what label fits Barack Obama?

His enemies on the right portray him as a flaming liberal, but how does that square with the 30,000 additional troops he's ordered to Afghanistan? Or with the full-page newspaper ad taken out over the weekend by the American Civil Liberties Union, portraying Mr. Obama morphing into George W. Bush because he seems to be shifting rightward on the question of trying terror suspects?

That shift on terror policy, in fact, seems to be feeding the Obama-as-pushover view that appears trendy at the moment. He came into office pledging to overturn the Bush-era policy of trying terror suspects in military tribunals. But the decision to use a civilian court for the most notorious of terror suspects, Khalid Sheikh Mohammed, set off a firestorm, which is prompting the administration to reconsider.

If Bill Clinton could be neatly characterized as a New Democrat, and George W. Bush as a compassionate conservative, what label fits Barack Obama? Official White House Photo by Pete Souza

Thus, those on Mr. Obama's left grumble that he isn't showing the spine needed to stand up to vocal proponents of the Bush-Cheney policies on terror suspects that he once campaigned against. "As president, Barack Obama must decide whether he will keep his solemn promise to restore our Constitution and due process, or ignore his vow and continue the Bush-Cheney policies," declared the ACLU's weekend ad.

Meantime, those on the president's right grumble that his lack of toughness led him to cower before Beijing by declining to meet the Dali Lama, a perpetual thorn in China's side, until after Mr. Obama first held a summit meeting with Chinese leader Hu Jintao last fall.

Similarly, those in the center complain that President Obama has allowed himself to be pushed around by his own party's liberals, first by allowing the House's Ms. Pelosi to shape economic-stimulus legislation last year, then by letting himself get maneuvered into a full embrace of a politically doomed public option, or government-run health-insurance option, as part of his party's big health-overhaul plan. Moreover, they complain, it took Mr. Obama a full year to present and vigorously defend his own health-care plan, rather than simply fall in line behind bills written by congressional Democrats.

Yet this view of a president lacking in toughness doesn't square with other evidence on the table. If Mr. Obama was shrinking from a fight with China, he could have avoided or diminished his recently announced $6.4 billion arms sale to Taiwan, which has elicited howls of protest from Beijing.

On health care, after an initial courtship hit the rocks, he has picked a fight, and a big one, with the nation's insurance companies, perhaps the most potent adversary around, and the one that pretty much killed off former President Bill Clinton's health-care plans in 1994.

Mr. Obama kept up his high-profile feud with insurance companies Monday, declaring in a speech near Philadelphia that they will keep raising rates until legally stopped. "How much higher do premiums have to rise until we do something about it?" he asked. Certainly Mr. Obama has made a strategic choice in demonizing insurance companies, which carry approval ratings on a par with those of used-car salesmen, but they are a dangerous foe nonetheless.

More surprising is the president's willingness to pick a fight with an interest group that's clearly part of his Democratic coalition, the teachers unions. Mr. Obama, who has encouraged states to crack down on underperforming teachers to improve their chances of winning more federal aid, stunned the unions last week by endorsing a decision by a school district in Rhode Island to fire all the teachers in an underperforming high school.

Perhaps the most intriguing bit of Obama toughness is the one that gets the least attention, because it unfolds in the distant nether regions of Pakistan. There, the president has authorized a dramatic increase in airstrikes by American military drones against Taliban and al Qaeda leaders and their hideouts.

Whether this escalation in American strikes is a cause of, or a result of, a firmer stand by Pakistan's own government against the Taliban is unclear. And it may not matter, for either way the result is a tougher posture in one place where there may be no substitute for toughness.

Write to Gerald F. Seib at