First, you have a good idea that you can get a feel for things with a smaller sample, to work out the kinks in your approach. And it's definitely true, as you've noticed, that things that take a while to run really break up your focus. It's annoying. But...
Second, you have to define "interactively". Do you mean instantaneously, 1 second, 10 seconds, or what?
Third, you need to account for your hardware, the software you're using, how much data you have, and what algorithm you're executing.
For example, doing an
lm on 100K rows of data might be "interactive" for you. Obviously
glmnet is doing a lot more than that.
In terms of other languages, Python or Java may be faster if you have a lot of code outside of
glmnet that you're executing. As one of the comments says,
glmnet is coded in C or Fortran and will be as fast as possible. If you're doing looping or a lot of code around your
glmnet, it's easier in R to do something inefficient than it is in programming languages not designed for statistics like Python or Java.
It's possible to parallelize some algorithms. I'm not sure if
glmnet is one of them. If you find a language that has a parallelized version -- say one that uses multiple cores, and you're running on a machine with multiple cores and enough RAM -- that will speed things up sub-linearly. Four cores won't be four times as fast, but it should be 2-3x faster.
So, the answer is "no, probably not". Your algorithm will usually trump anything else, and perhaps
glmnet alone isn't the best option.