Obama is Republican. Is he still president?
Not if he was elected in 2008; the term limit comes in.
Well, what's the PoD? It's very unlikely that Obama would become a Republican. His mother was a leftist; his childhood mentor was Communist Frank Marshall Davis. His college associations were left-wing, both at Occidental and Columbia, and at Yale Law. His associations in Chicago likewise - the New Party, Ayers and Dohrn. Virtually all blacks in this period were Democrats.
But let's go wild. Suppose that he had some road-to-Damascus epiphany, and became a conservative in college. Maybe he visits Cuba, and stumbles into the reality of life under Castro - and
all of his leftist friends either deny the facts or openly excuse Castro's crimes. Then he meets some Vietnamese refugees, and the cognitive dissonance increases. His then-girlfriend is persuaded to turn lesbian by some militant feminists. He says some "politically incorrect" things, and is viciously condemned and ostracized. He's left wandering.
That would be around 1980.
So he goes to law school, but at U. of Chicago, not Yale... He meets some libertarians, reads some Ayn Rand, meets some evangelicals and finds they aren't the cartoons he was told they were. By the time he graduates, he is more comfortable with Republicans than most Democrats.
He gets hired on to a major law firm in Chicago and does well. He marries the sister of a Jewish colleague, and converts to Judaism himself. He has Israeli in-laws, and visits Israel.
By the 1990s, he's living out in predominantly Republican Lake County, and gets modestly involved in party activities through his wife. In 1998, he's invited to be a candidate for state senator. He's supposed to be a sacrificial lamb, in a lopsided Democrat district, but the incumbent Democrat is old (and getting stupid), lazy, complacent, sleazy, and a hack. Obama wins in a shocking upset. His black and Jewish connections don't hurt at all.
The Democrats fumble the 2000 re-match - desperate for "youth", they put up a novice who bungles the campaign, and Obama is in for four more years. (Illinois State Senate seats terms are for 4-4-2 or 2-4-4 years in each decade.) In the state Senate, Obama gets a reputation as a "bomb thrower", challenging the bipartisan "Combine" of insiders. In 2004, establishment Republicans (their wing of the Combine) force Senater Peter Fitzgerald into retirement. (As in OTL - Sen. Fitzgerald earned their wrath for the appointment of US Attorney Pat Fitzgerald, scourge of Combine figures including ex-Governor Ryan.) Sen. Fitzgerald seeks revenge by getting Obama to run for the now open seat. Obama wins the three-way (originally four-way) primary when rival Jim Oberweis withdraws in his favor, and defeats Democrat Blair Hull, whose personal baggage sinks him.
Obama immediately becomes a rising star in the Republican Party. He sits out the 2008 Presidential election, having been warned of the potential economic bust coming, but does make a much-acclaimed speech at the convention. The Democrats win behind former VP nominee Sen. John Edwards. Obama makes a name in the Senate as a prescient critic of sub-prime lending, Fannie Mae and Freddie Mac, and now of "Wall Street/back street bailouts" (his term for Federal money to rescue big financial institutions and improvident mortgage defaulters). He's also an outspoken friend of Israel, a critic of illegal and barely legal immigration, and aggressively involved with "cyber" issues: requiring
effective security for government agencies, banks, and utility operations; fighting MPAA/RIAA efforts to abuse copyright; reining in "hacking" by the NSA and FBI; and so on. He's sound, but not publicly aggressive, on school choice, 2nd Amendment rights, and abortion.
The death of First Lady Elizabeth Edwards in September 2010 (three months earlier than OTL) blows the cork on President Edwards' extramarital affairs and bastard child. Mrs. Edwards had known for years, but kept silent, persuaded that her husband had broken off the affair with the child's mother and would be faithful, and would use his public office to "do good". She became disillusioned about the latter after Edwards became President and began cutting deals for cronies. She became really angry when in her last months, Edwards ignored her, and she learned of his affair with a clever female lobbyist turned White House deputy. She recorded a videotape stating all the facts, to be released after her death.
The tape leads to a Republican landslide in November 2010. It implicates not only Edwards' personal life, but his conduct in office - he had used official powers to buy or compel silence, with the conscious complicity of many important Democrats, and had also allowed Ms. Lobbyist to manipulate policy to her business associates' advantage. There are reports of her selling access and influence on a grand scale - she is compared to notorious Frenchwoman Christine Deviers-Joncour, the self-proclaimed "Whore of the Republic".
Obama is easily re-elected Senator in 2010. In 2012, he is elected Vice President as the running mate of ???? (can't think of who this should be). ???? is assasinated by jihadi terrorists in 2015. Obama succeeds to the Presidency, and is re-elected in 2016. So he's still President.