I don't know what the exact balance should be, but I would start low, rather than high. The number of people necessary should be low enough that 80% of the "bad bills" don't pass anymore, but also high enough that you don't have 80% of these oppositions as abuses of the law.
The reason I would start with a lower number first, is because we've already tried the "more representative" version of the Government, and it hasn't been working that well lately, and because it's much easier to get them to raise the number later if it gets too abused, than it is to get them to lower the number, because that would mean giving even more power to the people, and it's not something they'd like to do.
I'm not entirely sure how this opposition should happen - through signatures, I guess? But they should give a lot of information about themselves to verify them easily, or it needs to be done in such a way that a politician can't easily manufacture these to stop an opponent's bill.
Maybe this is a good suggestion, maybe it isn't. But I do believe that in the future we'll need more direct democracy influences on the Republic, for it to stay healthy. The Republic needs to be a lot more bottom-up than it currently is. Voting every 2 or 4 years to change a candidate, from the very few options, when in 98% (fact) of the cases those with the most campaign money win anyway, and then allowing them to do whatever they want when they get there, is just not enough anymore, and it's clear it hasn't been working well. This is why so many people are frustrated with the voting process and don't vote. They know it's mostly useless. The Republic needs to be upgraded for the 21st century.