The discovery of spies on the inside could have stopped the program in its tracks. The scientists would have been questioned, prevented from talking to each other, and so on while the situation was investigated.
This is a Gordian knot, people.
Go back in time and kill the time travelling historian’s grandfather.
Wouldn’t work.
The time travelling historian is his own grandfather!
clashing drums and cymbals
Didn’t Willie Nelson have a song about that?
[hijack] [sub]Sung to the tune of. . . you guessed it: “I Am My Own Grandpa”[/sub]
*"Many many years ago, near 1943,
I was working on a project, just as busy as could be. . .
This General had me on this bomb, it was secret from the Reds,
But Julius and Ethel gave it to 'em, hand delivered instead. . .
I work on the A-Bomb. I work on the A-Bomb. It sounds silly I know, but it really is so, 'cause I work on the A-Bomb.
Well, ol’ Joe Stalin surely did have himself a plan,
but we beat him to the punch when we let go on Japan.
Truman sure was in a spot, “Hey, should we build another?
Lest the Commie Reds make their own to threaten my dear Mother?”
I work on the A-Bomb. I work on the A-Bomb. It sounds silly I know, but it really is so, 'cause I work on the A-Bomb.
*
[/hijack]
My apologies, Mr. Nelson. 
Tripler
Sorry, Paul–I didn’t mean to turn this thread into a musical.
The President rolled his wheelchair from behind his desk and fixed his visitors with an unwavering stare.
“General Groves, Doctor Oppenheimer; I need to know what progress you are making on this “Philadelphia Experiment” project. Will it work or will it not?”
Oppenheimer made a helpless gesture with his fedora. “Mister President, we are forced to admit that we have reached an impasse. The best we have been able to do is to make a rowboat disappear from a wharf in Philadelphia. It re-appeared three days later, but in Butte, Montana.”
The President looked up from the cigarette he was fitting in its holder.
“Gentlemen”, he said carefully, “I think we should put this program on the back burner and get cracking again with the Manhattan Project. We have wasted six months, and I fear the Germans may be ahead of us, or will be soon.”
“Yes sir”, the two men said and, knowing they had been dismissed, turned toward the door.
“Oh, and not a word of this to Harry. He has no need to know. After all, he is just the Vice-President.” the President said airily, waving his cigarette holder.
(bolding mine)
Kissing each other was a common occurrence for these scientists? :dubious:
Los Alamos is an interesting place. 
It is doubtful that this would have stopped the program; in fact, there were numerous attempts to impose stricter security which were put paid to by Gen. Groves in the interest of expediency.
Under the confined conditions of Los Alamos–unmarried or unaccompanied scientists were living in dorm barracks, eating at a common mess, and working long hours (12+ hours a day, 6-7 days a week) in close quarters–even the only moderately contagious t.b. could have spread rapidly. A disease like polio or influenza would have passed through like a wildfire through chaparral.
Stranger
Franklin Roosevelt dies in 1943 and that pinko Henry Wallace becomes President.
The plot to assasinate Hitler succeeds, the threat of a German A-bomb disappears and all the refugee scientists lose their sense of urgency.
The scientists have all the uranium they need, but supplies of some other vital commodity are interrupted.
It turns out that “The Manhattan Project” is actually an attempt to get Rogers and Hart to write a new musical based on their 1925 smash “I’ll Take Manhattan”
Just a thought…how much help did your time traveler give to the A-Bomb project to get it started, early? Did he basically just say “oh, and that Atomic Bomb thing actually does work. You should probably get right on it,” or did he have any technical advice that he was able to pass on—possibly flawed or simply mis-remembered information, as you said he wasn’t a nuclear expert?
Maybe that, or other unintended effects from his starting the project early lead to more time being wasted on the “Thin Man” plutonium-gun weapon, before it was realized that it wasn’t workable?
Or perhaps, enchanted with the knowledge of future nuke designs, the Manhattan team tries to bite off more than they can chew with something more advanced (like a thermonuclear design, or a more efficient implosion setup) than what they originally would have built, before realizing they didn’t quite have the skills or the resources to pull it off just yet.
Depending on how involved he was in the project—he might have been kept out of the technical loop for security reasons, bureaucracy, or simply because he doesn’t actually have the in-depth scientific knowledge to be of much everyday use—he just doesn’t have the chance to say “wait, there’s your problem—that track didn’t work in the original timeline!” because he didn’t know what the specific delay was in the new bomb program, until valulable time had been lost.
Other ideas…
Maybe he points out who the Soviet spies in the project were, and G-Men come and drag 'em off in the middle of the day without a word—inspiring fear and protest from the rest of the scientists, and delays either from nervous inefficiency, or a deliberate work slowdown? They did seem a slightly idealistic bunch, at times—witness the letter urging Roosevelt not to drop the bomb in combat, but as a demonstration.
Might be an additional challenge (the fun kind, I mean) for an author, that—depicting the infamous asshole J. Edgar Hoover as ultimately acting completely within reason, and some of the finest scientific minds in the world who’re honorably concerned about the future of atomic weapons as ultimately acting like a bunch of flighty idiots!
Heck, just get Feynman involved earlier in the project. Feynman attracted a great deal of attention to himself, and caused a number of “problems” because of his hobbies. One of which was that he did codebreaking for fun, this caused the censors, who scanned every piece of incoming and outgoing mail fits, until they worked out a system with Feynman and his family wherein the family would send the key to the codes along with the letters, so that the censors could verify Feynman wasn’t getting coded instructions to blow up the place or something.
The other thing that he did was safe cracking. Feynman quickly realized that the locks on the safes were junk, and when his efforts to get this corrected through channels proved fruitless, Feynman went around popping open safes whenever he found them. It got so bad that the Army (in a perfect example of “military intelligence”) ordered anyone who’d had a recent visit from Feynman to change the combination to their safe. This made it difficult for Feynman to meet with anyone as they didn’t want to have to change the combinations on their safes. This gives you two simple vectors to play with, at least. One is that because so many people refuse to meet with Feynman, it slows everything down. The other is that because the Army does the smart thing, and buys better safes, it causes delays because folks have to entrust their documents to secure safes and can’t always get access to them, like they could if the safe was in their office.
One of the reasons it was chosen was because someone involved with the project had gone to a private school there as a child and loved the area. He was a classmate with William S. Burroughs, I’ll allow you to draw your own conclusions from that.
Does this setback have to be self-contained to the Manhattan Project? Would it be feasible to work in that your time-traveller has brought back some details on e.g. jet engines or RADAR that cause key personnel/resources to be redirected to mass-producing these (more tangible, less risky) technologies?
Perhaps side-track the project for a while to work on better computers?
Alternatively, you could just slow the project down to reflect the fact that it was started at the behest of a crazy negro-loving woman-liberating non-smoking pinko from the future? That’s got to be worth some bonus bureacratic heel-digging and obstructionism…
Otto Skorzeny hang-glides in and abducts Robert Oppenheimer.
Your readers won’t see that one coming.
Ranchoth is the winner I think.
They go with centrifuges, which delays the production of fissionable material. They go for an H-bomb right off the bat. (The egg-heads want to show they know more than the time-traveller gives them credit for.) Lots of resources are spent on the Yucca Mountain repository, and that slows things down too. A little here. A little there.
That ought to do it.
Thank you all.