brew install node stuck at `make install`

I had the same problem. Eventually, I understood that I didn't wait enough time.

To prove that this is the problem, just run it with the -v switch

brew install -v node

The make install step takes about 20-25 minutes.

Looking at the OP's terminal logs, the OP installed node using the --without-npm option. According to the Homebrew FAQ, passing command-line options to the brew install command triggers a source build of the package, which can take a while to run.

I suspect the OP is passing --without-npm so that his global npm packages are properly migrated when upgrading Node with Homebrew without any wonky issues. I used to do the same, but since --without-npm turns out to slow down node installation, my new solution is to choose a separate directory for global npm packages. Set the following in your .bash_profile:

export NPM_CONFIG_PREFIX=/usr/local/lib/npm-packages
export PATH="$NPM_CONFIG_PREFIX"/bin:"$PATH"

To ensure that future node upgrades with Brew don't trigger source builds, uninstall node completely and then install it again.

brew uninstall --force node
brew install node

Because this is a clean reinstall of node, you'll need to reinstall your global npm packages.