If you look at the positions of the two broad political coalitions in Lebanon, specifically with regards to Israel, you will not find much of a difference. Both parties agree on being the "last country in the Middle East to sign a peace deal with Israel." The opposition is calling for a return to the truce agreement that was signed after the 1948 war; Hizballah insists on not going there, but has participated in a de-facto truce since the Israeli withdrawal (with around 15 infractions - none of which were major incidents).
Hizballah's rhetoric indicates otherwise of course. But speeches to crowds should not be intepreted at face value, especially speeches from Hizballah. Their constituency is the most disadvantaged group in Lebanon. The Shi'as have suffered from poverty, displacement, constant Israeli harassment, and even scorn from fellow Lebanese. Reasons behind these conditions are geographic, historical (going back to the Ottoman Empire and beyond), as well as inherent political flaws that can be attributed to the formation of the Lebanese Republic.
This is not to say that Hizballah doesn't see Israel as its eternal foe. However, limiting our analysis to the "Arab-Israeli" conflict is too superficial. The Party of God would definitely beg to differ, and in doing so, they offer other Lebanese a tremendous favor by effectively channeling Shi'a frustration to an "enemy" that is outside of the country.
Therefore, although the political positions seem to revolve around how to confront Israel, there are other, more local, nuances at stake. The domestic message of the protests are "Hey, look at us: we're here! We count! We're saying that we hate Israel and love Syria; but what we really mean is: don't think you can ride the changing fortunes of regional politics without taking us into consideration - oh and by the way, we pretty much like things the way they were before Syria started packing up. Change (especially if it is tainted by anything from the 'West') is unwelcome."
The international message, on the other hand, is very clear from the rhetoric: "Israel, America, and any other entity that opposes Hizballah, don't think you can get rid of it! It has real popular support, and is a legitimate force in domestic Lebanese affairs. Short of full scale war, it just ain't gonna happen!"
As always, I don't know how things are going to pan out. Lebanon seems to be divided into two camps: the Western and Eastern. Although Hizballah is powerful, its leaders probably don't want to over-play their hand and completely isolate the opposition. They're also aware that a considerable proportion of the Shi'a population doesn't necessarily agree with their vision for Lebanon - hence the wise decision to focus the demonstration on the rejection of 1559 and "Israeli/Western agression," something that all Lebanese are probably united behind.
On the other hand, it has been made obvious that the opposition will need Hizballah on board if they want to go anywhere. Both sides have now flexed their muscles and earned their seats on the table. It's time for them to take a look at what is happening around them, and move forward.