Could modern weaponry defeat Spiderman?
For basically every version of Spider-Man, yes. The only version that would live something like a nuke would be Cosmic Spider-Man.
- Lifts a fully loaded barge
- Swats a car so hard it lands in the middle of New York Bay
- Takes down Goliath
- Breaks out of Quasar's constructs without any leverage
- Punches Hulk into orbit
- Does the same with Thor (Earth-91110)
- Throws toxic waste into the sun from outside of Earth (Earth-91110)
- Punches Terminus out of the solar system
- No-sells a power cable
- No-sells flame breath from Dragon Man
- Falls from a thrity story building right through the pavement and then attacked by Titania (She-Hulk level) and only feeling slight pain
- Shrugs off a beat down by Titania
- Tanks a Mjolnir throw by Thor (Earth-91110)
- Shoots down a lot of metal shards thrown at him by Magneto
- Enhanced reactions makes him punch away Quasar before he can examine him
Spider-Man is pretty durable even though damage resistance isn't one of his official powers, he takes some pretty huge hits and manages to keep fighting or recover. That said Spider-Man is NOT bullet proof and never has been, against guns and the like he relies on dodging (superhuman agility allows him to dodge bullets and energy blasts and such rather easily). Modern weapons are fully capable of killing him, but hitting him in the comics is very, very difficult.
Guns can kill Spider-Man pretty easily as long as the people shooting them didn't go to the Stormtrooper academy of missing. The amount of round a modern mini-gun or something smaller can put out in a minute make it impossible for even Spider-Man to hope to survive.