I know I'm treading in dangerous water here, but could Israel have made it all the way to the Jordan river in the 1948 war?
Maybe, but it would have been hard.
The West Bank's borders basically follow the Judaean Hills (save for the Jerusalem Corridor), and that's no coincidence. Even setting aside the fact that it was guarded by the Arab Legion (easily the best fighting unit on the Arab side in the war), the geography there is very difficult and by far favors the defender, with lots of rugged, often steep hills the emplace on top of. The Israeli push up the Jerusalem Corridor is generally considered to have been the toughest campaign in the war, and they did that by following the easiest path up through the mountains. In the 6 Day War, the fighting in the West Bank was arguably the toughest, and Israel won with heavy, heavy use of air support (which they didn't have in 1948) - also, the Jordanian army retreated after a few big losses rather than fighting for every inch of land. Which I suppose could also happen in '48.
If the war lasted long enough, I think Israel could have taken it, but it would have been a very slow and costly operation. Possibly Israel would be willing to pay the cost, but it would still take a long time (unless somehow a diplomatic accord was reached).