Since consumers of a cryptocurrency could be presumed to desire instantaneous transaction verification, is near instantaneous transaction verfication possible and secure? If so, how?
If by "instantaneous" you mean "right at the moment of the transaction" - well, no. Not even with Visa et al. Even if you mean that, after waiting for a reasonable amount of time (say, less than 2 mins.) you receive a definite answer about your transaction's validity, it's not possible either.
The way cryptocurrencies work, all transactions are "waiting in line" to be picked up by a miner and included in a block. Meanwhile, you can always revert it or create another that conflicts with the first one. Once a transaction's in a block, though, you can still not claim victory for they're still not part of the official coin history: other miners need to accept the block and start constructing new blocks over it - and this is the critical part.
Another miner, somewhere else in the world, may have discovered another solution to the current block and broadcasted it onto the network. From that moment on, there will be 2 chains in competition, both of them valid, but eventually only one will become the official one. Which one? Whichever gets longer first, i.e. which is picked up by the most miners to create a new block after it - remember each block contains not just its hash but also a hash of the previous block, so in effect each block "points" to its predecessor, hence the term "chains".
It's also possible for a malicious part to do this on purpose - should that part have access to vast amounts of computing power it could convince you to give you something in exchange for their bitcoins. You see their transaction appearing in 2 blocks and give the stuff, they then take the last block before your transaction appeared and rapidly create 3 blocks without the transaction. Once they broadcast their 3 blocks to the network - voilá! Their chain takes over due to length, you end up with no item and no coins.
So you never get a definite yes or no answer - you just get degrees of certainty. The more blocks your transaction appears on, the more likely it is that it will be part of the official transaction history. That's why it's commonly said you should wait for 6 confirmations in Bitcoin or 12 in Litecoin to consider a transaction 99% valid - after that number, the probabilities of an attacker trying to out-run (so to say) the combined hash power of the whole network become almost negligible.