When Queen Amidala asked the Senate for aid in The Phantom Menace, just what was she expecting them to do?
Before Attack of the Clones came out, I would have said that she expected them to send part of the Army of the Republic to Naboo. But now we know that at the time there was no Army of the Republic. So what was she expecting? A talking-to and a time out for the Trade Federation? Considering that she decided on "aggressive negotiations" to free her planet, I don't think that's what she had in mind.
What has the Senate done in the past, or what are they supposed to do in such situations? Since the Jedi didn't fight wars for people (yet), I see two possibilities. The first is that the Senate would order the police, probably from systems near Naboo which were able and possibly Coruscant as well, to handle it. This would leave at least one planet, probably several, short on police, and who knows how much training and firepower the police actually had anyway, but as the Trade Federation is part of the Republic, the Senate might see the police as the proper response. The second is that since the Trade Federation had (most likely) broken the terms of their admission to the Republic by invading a fellow member's territory, the Senate would declare the Federation's Republic membership void and rustle up a coalition of planetary armies to force the Federation off Naboo. Like the police option, this would leave several planets stripped of their defenses, which is risky, especially when you consider what a certain crafty senator could do with such an oppurtunity, but the Republic was complacent.
And then there's still that pesky issue of getting proof before galavanting off to Naboo with big guns. I mean, really. Did Amidala expect them to just send off the troops (or cops) on her say-so? Imagine the Republic is the British Commonwealth, Naboo is Canada, and Amidala is the teenaged prime minister of Canada. She waltzes in one day and says, "Help! NAFTA forces have invaded my country!" (Not an exact parallel--since the British Commonwealth, in addition to not having an army, doesn't have any actual authority--but you get the idea.) Do you, as a responsible legislator, reply, "Okey-dokey, we'll be right there," or do you ask for satellite pictures and video and the serial numbers from the tanks first? Just because it's the Federation representative asking for an investigation doesn't mean it's a bad idea.
Furthermore, even if the Senate voted to go to Naboo immediately, they wouldn't be able to actually go immediately. No Army of the Republic standing by, remember? First they would have to decide whether it was a police or a military matter. Then they would need to know exactly what the Trade Federation had on Naboo--how many ships and what kind, how many battle droids, etc. Otherwise they wouldn't know what to send, would they? Then they would have to put together a multiplanetary force. Just working out the chain of command could take a while. They would have to go through all this sure they wouldn't send too many or too few troops or have any organizational snafus that could cost them the battle when they got to Naboo. To expect them to respond instantly is extraordinarily naive, desperate, or both.
Of course, if Amidala had waited for the Senate, it might have been too late to save Naboo--and that's if Palpatine hadn't manipulated the Senate into voting against doing anything. That she would go back, ally with the Gungans and their secret army, destroy the droid control ship, capture Nute Gunray, and force the Federation to leave Naboo was a shock to everyone involved. The Nemoidians certainly didn't see it coming. If we had been able to hear Nute Gunray's thoughts during his communications with Amidala (or whomever she delegated to talk to him, since hearing from Amidala herself was "getting results"), they probably would have gone like this: "You're going to make us end this blockade, are you? You and what army?"