I’m a simple man, not especially musical, although I did play a pretty mean sax back in middle school, and took my share of piano lessons (never got the hang of the left hand), but I’m always in awe of the fact that Paul McCartney was able to play this, while singing this.
Am I just easily impressed, or is this truly as remarkable as I think it is? Did it just take a shitton of practice for him to get it down? Or did he simplify the bassline during live performances?
Playing an instrument while singing is always a challenge, but the ones that do it for a long time get very comfortable. Keep in mind that McCartney and the Beatles spent many years playing crazy long gigs every single night before anyone outside of Hamburg knew who they were. To the public they came out of nowhere, but they were very seasoned veterans by then, which shows especially in their harmonies. What McCartney does on “I Saw Her Standing There” isn’t exactly remarkable; the song is a a pretty simple three-chord song. But that’s not to diminish the performance. He nails it.
Don’t know if that helps to answer your question at all. 
I’ve been playing the bass for years and consider myself something of a virtuoso. Paul has made some cool bass lines but I don’t really see anything too impressive here honestly though.
This is a very simple and repetitive bass riff, pretty much the perfect kind to sing along with, though I do give props to any musician that can play an instrument and sing at the same time. Of the bass lines that I can sing at the same time while playing, it’s kind of a funny sensation mentally because it’s like your fingers really just go on autopilot and then you sort of take a step back and focus on your vocals. I’m always impressed especially by drummers that can sing at the same time, I think that really takes a lot of talent.
I suspect that everyone who tries to sing while they play the first time, will find it insanely difficult, but almost everyone learns.
As for McCartney, he has some unusual playing techniques. You might look online for some of his small schoolings. As with Ringo, he occasionally shows exactly how he plays something, and a few times, I’ve been more or less shocked by how he manages to do it, using rather crude fingerings. No questioning the results!
One of my favorite McCartney bass lines: the one on “I Will,” from the White Album. Only fingering impossible to do live.
It is a (wonderfully) busy bassline, but it stays in time, in a steady groove. Once you get that burned into your brain and muscle memory, you can add stuff to it, like singing.
It is like juggling or riding a bike, but with the groove of the music as a guide. As you play that steady bass riff, you learn to know exactly when to “toss your voice in” so it is sync’d up properly.
It’s fun and a bit of a high, really. You get in the zone, all the pieces you have mastered individually and have solid muscle memory for are coming together, and you are kind of stepping back and just overseeing whether each bit kicks off at the right time relative to the others. When the gears all mesh, it can be transporting. Which, strangely enough, helps you sell the vocal, because you feel strong emotions because you are locked into the groove, and you direct those towards the vocal, if that makes sense.
I’m a keyboardist by trade, but it doesn’t seem particularly difficult to me, given that (as stated), it’s a straight boogie woogie type of bassline with a constant flurry of notes, so no crazy syncopations or anything like that. I would expect any decent bassist who also sings to be able to hack it. Guitarists do this sort of thing all the time, as do pianists (with even more intricate interdependent parts going on.) I also don’t find drumming and singing at the same time to be particularly more difficult than any other instrument, to be honest. What I do find difficult, though, is maintain a perfectly natural sounding conversation while playing an instrument. I can talk and play piano or guitar or drums at the same time, but there are occasional unnatural pauses, because the flow of conversation is not synched rhythmically to music the way a sung melody line is. It depends on the part, though. A boogie woogie left hand bassline I can talk over in a natural pace, but something like Maple Leaf Rag, I need to throw pauses in here and there.
Didn’t you mean to say “but some… thing like Maple Leaf, Rag I. Need to throw… pause… es in, here. And there”.
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^ Take anothr look, the sentence reads fine.
Little to add to the solid responses upthread. I think it’s pretty good playing for 1963, in that style and considering he was 21 years old that year. I like the focussed transmission of positive energy. It seems to come easily to him, which might draw criticism from some, but he’s no slouch and his positive attitude is an important part of his playing, in my opinion.
That actually is a pretty reasonable approximation of what it sounds like. 
I also grew up with church organists playing a foot part, a left hand part, a right hand part, and singing over all of that, so I may be a little harder to impress. 
But, seriously, the bassists I’ve played with would be able to handle that line pretty easily. But they were, I admit, very good bassists, some of them fronting their own bands, so they were used to playing and singing at the same time. It’s a great bassline, and a great song, with one of the best opening lines of any rock song anywhere, but it’s not like some sort of virtuoso wizardry to play that bass part and sing it at the same time.
Thanks for the solid replies and info. I’m just easily impressed!
It’s based on Chuck Berry’s “Talkin About you” as per Paul himself.
pulykamell, I seem to recall, no cite sorry, that having a conversation and playing music uses very similar parts of the brain and is therefore very difficult (I find it difficult too), but singing is not something that requires thought in the same way a conversation does. When we sing and play it is essentially processed as a single activity by the brain, or something.
Seems to me that there’s a lot of repetitive figures in there, which would be easier to learn. As long as you’re effectively doing the same thing over and over, it becomes pretty easy to sing over it. It’s when you do something different that you might have think and then could get your fingers and your lips figuratively tangled.
Same happens to me with left hand and right hand on keyboard. If I can put one or the other on autopilot via repetition, I can concentrate on changing the other. Usually I do this for the left hand, so I’m not as good doing it on the right hand.
I wonder whether rapping is closer to singing or conversation in this respect. Are there any rappers who play instruments while they rap?
Funny, I thought about speaking to something like this but didn’t because I talk too much in music threads as it is.
Here goes: I think of it, as I said upthread, like juggling. It you have three normal juggling balls, you just juggle. But if you have two balls and a chainsaw ;), then you depend on things being easy with the balls and you’ll pay attention to the saw, right?
So - if the vocal is hard, with phrasing and words and stuff ;), then that’s your chainsaw, so you hope the music you’re playing is pretty on-beat, like that Beatles bassline.
I perform Aerosmith’s Walk This Way. In its case, the underlying guitar groove is a syncopated boogie shuffle that requires a bit of attention to stay grooved on. Ah, but the vocals on the verse are pretty much rap - Run DMC would agree with me - so the vocal becomes the easier ball to juggle while I deal with the chainsaw guitar part.
Does that make sense?
Yes, it does, thanks.
Gotta strongly disagree with this. Walk This Way is not only fast and wordy, it’s melodic and deceptively difficult to sing right. I’ve heard a lot of bar bands attempt it, but only a few who could pull it off. It’s funny, but just yesterday a student at the high school where I work was playing the Run DMC video on YouTube, and the first thought that popped in my head was “God, I’d almost forgotten how they sucked all the life out of that song.”
I dismissed Paul as a pretty face, but listened to a lot because folks here insisted he was great. I was amazed. No maybe about it.
I think part of it is that when you converse you have to think of what to say and say it. When you sing though, the words are already there, all rehearsed. You must remember what words to sing but you don’t have to go through the mental process of translating originals thoughts into words and then speaking them.
There is that, and also the fact that the words are said in rhythm to the music, too.