Could the UN have come in and declared UK government unfit*, and Obama is acting as a temporary leader until one can be found?
* can the UN do that?
Not in real life, but the United Nations in the Whoniverse has previously been established to possess greater authority than it does in the real world -- the existence of U.N.I.T., the
Valiant, having provisions for removing a sitting head of government from office if he breaks U.N. treaties, etc.
But there's no evidence that the U.S. President in the Whoniverse is ruling the U.K. In real life, frankly, the President of the United States
is the world's most powerful person, and this episode just reflects that fact.
Having said that, the fact that the U.S. President is Barack Obama is interesting. In "The Sound of Drums," set in 2008, we met U.S. President-elect Arthur Coleman Winters, whom the Master later assassinated. One might presume that in the Whoniverse, Obama was Winters's vice presidential candidate who then assumed office on Inauguration Day 2009 as per the 20th Amendment.
I suspect that that might not be the case, however.
Torchwood: Children of Earth rather firmly establishes that the U.S. military (with the acquiescence of U.N.I.T.) staged an unofficial coup against Her Majesty's Government in the U.K., taking control of the British Army away from the Cabinet and Prime Minister from within Downing Street itself. The U.S. military then ordered the British Army to abduct 10% of the United Kingdom's children for the 4-5-6, and it is implied that the U.S. government was doing the same thing to its own people. So in
Children of Earth (which I would presume was set at least one year after the Dalek Invasion, in order for the invasion's chaos to be cleaned up), the U.S. President is implicitly cast in a villainous role.
Yet here, President Obama is seen in a thoroughly positive role. Indeed, the way the character is portrayed, I'm tempted to see him as perhaps being analogous to Prime Minister Harriet Jones -- the relatively heroic politician. Now, there's some question as to when "The End of Time" is set relative to
Children of Earth. Myself, I'm inclined to make things as chronologically simple as possible, and assume that
Children of Earth was set in the summer of 2010, about one year after the Dalek Invasion in the summer of 2009, and that "The End of Time, Part One" is set on Christmas 2010, about six months later, since I like to presume that apart from the one-year gap, episodes take place relative to one-another roughly as far apart as their airing dates.
That raises the question of whether or not Barack Obama was the President who implicitly ordered the abduction and enslavement of millions upon millions of British and American children and illegally seized control of the United Kingdom in
Children of Earth.
Given Obama's seemingly heroic role in "The End of Time, Part One," I'm inclined to think that we're
not supposed to assume that he's the same guy as the unnamed President in
Children of Earth. That raises the question of just how Obama managed to become President in the Whoniverse. We do know that the 4-5-6 affair forced the British Prime Minister to resign from office once the crisis was over; perhaps something similar happened with Winters's unnamed successor?
Now, I'll happily admit that this is partially because I'm politically biased as a Democrat and an Obama supporter, but I'm inclined to speculate that Winters -- with his Bush-like American chauvenism -- was the Republican candidate for President in 2008 who won the election. Winters, I would speculate, was then assassinated by the Master aboard the
Valiant before taking office while serving as the United Nations representative of Earth to the Toclafane, and was succeeded by an unnamed Republican who took office on 20 January 2009. This unnamed successor -- let's presume it's John McCain, just for simplicity's sake

-- would then have been the President in office during the 2009 Dalek Invasion. Now, I for one am surprised that the White House would have survived the invasion (though considering how
small the press conference room was in "The End of Time," perhaps it didn't and it's being rebuilt?), and I'd also be awfully surprised if President McCain were to survive the Daleks. But either way, he or his successor -- presumably a Republican chosen to replace Winters's VP who was then confirmed by the Congress -- would then have been in charge a year later during the 4-5-6 crisis.
I can easily see a crisis of that magnitude driving all sorts of political leaders from office in the aftermath, especially if any were involved in or complicit in the scheme to kidnap children for the 4-5-6. Perhaps a whole
swath of leaders, from the White House and the House and Senate leadership, were forced to resign and/or faced criminal charges -- the Speaker, the Senate President Pro Tempore, the Majority and Minority leaders, the entire Cabinet, etc. In that sort of political chaos, legally, the first person to get elected either Speaker of the House or President Pro Tempore of the Senate would instantly be elevated to the vacant U.S. Presidency. Perhaps with the House in chaos, Senator Obama managed to whip together enough of the still-officiating Senators to get himself elected Senate President Pro Tempore, thereby instantly elevating himself to the Presidency?
Not exactly democratic, but not exactly undemocratic either. Certainly it's fair to say that the crises foisted upon it by the Whoniverse -- Time Lord assassinations, Dalek invasions, alien extortion plots -- might simply have overwhelmed the American government and led to a great deal of political chaos. A charismatic and reassuring figure like Obama would probably have generated as much attention and admiration as he did in real life, if not more so -- and given that, the idea that Obama would be spoken of so admiringly if he had only recently come to office as of Christmas 2010 is not unreasonable.
Of course, there are a lot of ways we could play around with all this, including assuming that
Children of Earth actually takes place
after "The End of Time," since there's no explicit date for that one that I can recall. But it's all in good fun to speculate like this.
Oh, and I mean to say earlier, people talked about Heath Ledger being a brilliant Joker, and he was, but Simm kicks the crap out of him...
... No, he really doesn't. They're not even similar enough characters to compare them.
Think about it, right now apparently Sarah Jane has turned into the Master. So has Gwen. So has Martha. So has Mickey. So has every single other character we've ever met. So has every two year old still in diapers (not an image I particularly relish, there). What's going to happen? At the end, everything will go back to normal and no one will remember because it would be too ridiculous for them to keep any sort of real consequences from this absolutely crazy scenario.
Actually, they've pretty firmly established that everyone now knows about aliens and invasions and that the governments of the world have given up trying to hide it all. But what consequences would there really be? What would actually happen, other than that the economy would probably still be shit?
The governments of the world would say, what? "Well, an alien turned us all into one of him, and then another alien reversed it. We're working on a way to stop it from happening again, but, uh, yeah, remember when the Dalek invasion decimated every single military on the planet? We're not really powerful enough to fight aliens yet, but we'll try. By the way, do you think we should go to Mars and name our base there after Major Tom?"
I'm only 20 minutes into it, and it looks promising for the most part, but, I've got to say...
I have never, ever said this before about modern Doctor Who. Even at its goofiest or lamest, I could usually go with it long enough to just enjoy the episode.
But when they started spouting off about "the Secret Books of Saxon?" And then Lucy started spouting off about how she'd been preparing for his return, too?
I just sat there, with my mouth agape, and shouted at the screen:
"WHAT THE FUCK IS THIS SHIT?!"
Holy shit! If that's your response, Sci, then this episode may indeed be as bad as I thought it was while watching.
Yeah, that really is saying something coming from me, isn't it?
Actually, I liked pretty much everything
else about this episode. Really, I did. I love Wilf and seeing him as the Doctor's proper companion was wonderful.
But that entire sequence was just
godawful. It really was the absolute worst thing that nuWho has ever produced.
Ever. All five minutes of it were even worse and more painful than "Fear Her."

And it's really a shame, too, because it's a
horrible waste of Alexandra Moen, who is not only an absolute sex goddess but an
amazing actress.
Oh well.
The bit about the Master having superpowers was weird and I could have used an explanation, but it didn't bother me overly much.
Really, the only other thing I didn't like about the episode is the very idea of bringing back the Time Lords. I hated it. Always have and always will. The Doctor is just not as interesting to me if he's not the Last of the Time Lords. I really hope they're all gone by the end of "Part Two."
ETA:
Oh, and their Obama impersonator was rubbish. Really, BBC? £4.3 billion Crown corporation and you couldn't find a better Obama impersonator? Someone who actually, y'know,
looked like him?