Interesting question — to me, at least, and maybe even to Bryan. Here’s my response, with a few links added:
Did I say that? (Some context would be nice. No I don’t remember saying that.)
Technically, can’t happen now with the 25th Amendment and succession laws; if a president dies, another is there, probably without regard to swearing in.
A few historical examples suggest no big problem; these are nullified if missiles are in the air at that moment, though:
1. When Tyler succeeded Harrison 1 (first death of president in office), John Tyler was more than 24 hours out of Washington. Worse, many people thought that while the duties of the president fell to the VP under the Constitution, that should be a temporary condition settled by a special election. Despite all this uncertainty, nothing bad happened in the interim.
U.S. Sen. David Rice Atchison, from Missouri; photo taken by photographer Mathew Brady at the United States Capitol at Washington, D.C., March 1849. Courtesy of the Beinecke Rare Book & Manuscript Library, Yale University, via Wikipedia. Photo taken the same month some say Atchison was acting President, for one day.
2. On March 4, 1849, [James K.] Polk’s term expired. But it was Sunday, and incoming Pres. Zachary Taylor refused to be inaugurated on Sunday. So did incoming VP Millard Fillmore. Some argue that David Rice Atchison, the President Pro Tempore of the Senate and then-third in line for the presidency under the laws then existing, was president for one day. He didn’t claim that, but in any case, spent most of the day sleeping, as the outgoing Senate had been working late for several previous nights. Some argue that because the Senate had adjourned sine die on its last session, not even Atchison was president. In any case, nothing happened.
Official Senate bust, President of the Senate, Vice President Chester A. Arthur (it’s a bust; he was not really that pallid) Photo from Wikipedia
3. When [James] Garfield was shot, he did not die immediately, but hung on for more than a month before infection took him. Vice President Chester A. Arthur did not assume duties of president, nor did anyone else, in that period. A lot of stuff got delayed, but no big deal. Government continued during the long dying process, and until Arthur was sworn in.
4. Similarly, when [William] McKinley was shot, they thought he’d survive. VP Teddy Roosevelt took off to hunt in the Adirondacks. When McKinley took a turn for the worse, guides had to be dispatched to find Teddy climbing a mountain (Mt. Marcy); by the time he got to Buffalo, McKinley had been dead for several hours. Nothing of consequence happened as a result of there being no president on hand (and they were in Buffalo, New York, not Washington, anyway).
5. Woodrow Wilson suffered a stroke on October 2, 1919, that left him blind in one eye and unable to walk. He was kept out of the presence of the VP and cabinet for months; when he finally returned to cabinet meetings in 1920, he was clearly unable to function as president. It’s an interesting case with his second wife essentially taking over the office under the guise of intermediary and care giver to the president. This one may have had some consequences – the Senate never did ratify the Treaty of Versailles, for which Wilson was campaigning when he was stricken, and so the U.S. never joined the League of Nations, dooming it to failure years later as World War II erupted. But perhaps Wilson couldn’t have gotten it ratified had he been fully active, anyway. Perhaps Wilson could have influenced the election of 1920, which Warren G. Harding won (who would die of a heart attack in San Francisco, making Calvin Coolidge president). But all of that is pure conjecture.
6. The funniest (in retrospect) was when Ronald Reagan was shot. At a press conference at the White House as Reagan was being prepped for surgery, a reporter asked some cabinet officials “who is in charge?” Perhaps reacting too much to the question as a challenge to whether the government was leaderless and vulnerable, Secretary of State Al Haig grabbed the microphone and said “I’m in charge here!” In reality, Vice President George H. W. Bush was in full communication mode of the modern presidency; control of the “football,” the nuclear strike code case which accompanies the president at all times, could have been an issue, but was not.
President Obama at an airport; the Marine in the background looks to be carrying the “nuclear football.” Photo from Cryptome (Is this an AP photo? Anyone know?)
Under the 25th Amendment and the Succession Act, it’s difficult to imagine how the U.S. could be without a president at any time; the confusion around the death or disability of a president offers a window of a de facto gap, but that should last only minutes under the procedures and precautions now in effect (some of which we saw on 9/11).
Worst that could happen now? If missiles were incoming, and confusion over who has control of the football went on for more than 10 minutes, a retaliatory strike could be late in getting launched. It takes about 15 minutes for intercontinental ballistic missiles to get to their downward path, or to register on known radar, so a ten minute delay might be encouraging to a Russia that hoped to knock out the U.S. before a retaliatory strike could occur; but that’s probably not realistic. And, even that would be of no great consequence if the secret “missile net” many people think the U.S. has, actually exists.
Is this a class question, or are you involved in some odd drinking game again?
(Anyone else seen the movie? Is it a scenario not already contemplated under the 25th Amendment?)
Posted by Ed Darrell 
Millard Fillmore's Bathtub 