We can only begin to identify "slender threads," turning points or fateful decisions of the Obama presidency because he's still in office and we are not yet privy to behind-the-scenes thinking and internal debates. But at least the short-term consequences of some policies are clear, as Paul Krugman pointed out in an early January 2016 column titled "Elections Have Consequences."
Obama's victory in the 2012 election led to
a) significant tax hikes on the wealthiest Americans;
b) a significant reduction in the number of uninsured Americans, by (so far) 17 million.
Both of these changes have reduced the deficit and strengthened progressive priorities.
"If Mitt Romney had won, we can be sure that Republicans would have found a way to prevent these tax hikes. And we can now see what happened because he didn’t," Krugman writes. And Republicans, if they had won the presidency in 2012, vow that they would have repealed Obamacare.
The Economist in mid-2013 published a column speculating on how a Romney presidency would be different. He would have somehow convinced corporations not to hoard cash, which Republicans claimed was because business leaders lacked confidence in Obama, and they would start spending or investing immediately in workers and expansion. (This actually did happen under Obama, albeit more slowly as economic conditions and consumer demand improved.)
Romney would have proposed, according to aides, "immediate, 5% cuts to public spending excluding security and social payments (though more money for defence), a weakening of the rules that Republicans say favour trade unions, a squeeze on public-sector jobs and pay, and a global push for free trade. Mr Romney would also have proposed lower income- and corporate-tax rates, offset by closing loopholes." In other words, the deficit would be higher.
Quora.com has an ongoing discussion, "If Romney Won in 2012." Clearly there would be no policies to address climate change and the U.S. would not be moving aggressively toward alternative and renewable energies. Dirty coal would be back in favor. Some speculated that the Keystone Pipeline would have been approved, but that was taken off-line largely because of low demand.
It's unlikely Romney would have sought to open diplomatic relations with Cuba, and would most likely have rebuffed five other nations -- China, France, Russia, Germany, and the UK -- by rejecting the Joint Plan of Action to reduce Iran's nuclear program in exchange for reduced economic sanctions.
Some Romney aides claim there wouldn't be an ISIS. Oh really? Because the U.S. would have sent thousands of ground troops back into Iraq and Syria to smash ISIS, fill the power vacuum and occupy those countries indefinitely until stable governments developed? Now that would be really popular with the American people (NOT). So Romney would be running for re-election in 2016 having brought back another U.S. quagmire in the Middle East?
Steve Benin: "I realize Romney and his party are in a tough spot. They’re not exactly able to say, “If Romney had won, we’d see a big drop in unemployment, cheaper gas, and much stronger economic growth,” because Obama won and we got all of those things anyway."