Nero might not be much of a warrior, but if there's one thing he did know with perfect clarity, it would be the strengths and vulnerabilities of his mining hardware.
It cannot have come as a surprise to Nero that handguns would defeat his attempt at inserting red matter through a planet's crust. But he may have had misconceptions about how easy or difficult it would be to bring handguns to bear on the drill. Spotting the three skydivers without advance warning might be beyond the capabilities of the mining ship's sensing systems (although they should have been seen ejecting from the shuttle that must have been at the very focus of those sensing systems). But if Nero couldn't see the skydivers, it should follow that all sorts of small aircraft could get past him as well - and he should probably realize that.
On Earth, a hand phaser might not have hurt the drill enough. But there's a Starfleet installation right under the beam, and it would be implausible to think there wouldn't be armaments there. Not dedicated anti-boring-machine-from-the-future weapons, but generic stuff that would more than suffice. Say, if even one of those shuttles was left unlaunched when the cadets flew off, it could have been piloted to the drill and, if necessary, rammed into it. End of Nero's Plan A (although he could then rain red matter on Earth's surface and seriously inconvenience mankind).
Nero might not be privy to Starfleet strengths and weaknesses - he wouldn't have had much time to go through the information he tortured out of Pike, and he might not be skilled enough to put together what he got from his possibly hundreds of previous captives. But Nero would know his own strengths and weaknesses, and would realize that one doesn't need Starfleet to foil his plans. A fellow Romulan miner could have done that with Romulan mining gear, and Nero could absolutely count on Earth having at least something comparable.
Timo Saloniemi
P.S. There's another interpretation of the Vulcan scenes that makes the drill less vulnerable. Perhaps the rifles fired by Kirk and Sulu did nothing to the drill? Perhaps Nero's henchman simply chose to stop drilling, because he had reached his target - and afterwards reported to Nero that oh, there had been some sabotage there as well, nothing of consequence, the plan is moving smoothly.