The had good reason to believe they would be able to dominate the assembly completely. Though the third estate had twice the number of representatives, the voting was done by order and not by head, leaving the votes two against one. Both first and second estates went out guns blazing and demanded that they wouldn't lose any of their privileges and wanted all tax hikes to be placed on the commoners.

How much power the church had over the priests varied a lot, both because of rank and class (the higher clergy were exclusively noble and very privileged) but also by region. Later on this split becomes clearer with the introduction of the civil constitution of the clergy, which every member of the clergy was made to swear to or risk deportation or even death. On the other side of the coin, swearing to a constitution that denies official church policies would have been an enormous no-no for an obedient church member, but the percentage who took the oath ranged from 80+ to less than 35% in more conservative areas. I think you can assume that those numbers would correspond somewhat to the number who would be willing to support the more reform-willing in the estates general.

The estates weren't a sovereign assembly, and officially all power was still with the king. Legally, he had the power to dissolve the estates whenever he pleased. In reality the king was weak, since the armies he would have wanted to use to enforce his will on the population wasn't willing to fire on dissenting Frenchmen, and the population was willing to fight back. That's the real reason the third estate ended up with the power, not the official power given to the representatives. And the nobles had no way of knowing this was going to happen, so they probably expected the king to keep absolute power in the foreseeable future.

And the Parlement didn't really have legislative power officially either, and were only supposed to do what the king told them, so their power wasn't 100% to begin with. The king could still legally force them to act in a certain way, and he might force them to start paying taxes. They had popular support when the king did this, which might have given them the impression that the people would still support them in the estates general, even with their extremely conservative goals.

I'm going to offer an alternate explanation. Not everything the other poster says is wrong, but much of it conflicts with what I understand to be the prevailing view of period scholars. As an undergraduate I did a paper in which I was required to reconstruct a historical argument from my own use of primary sources, the topic I chose was the class character of the initial stages of the French Revolution and the sources I had to work with were Cahiers de Doléances.

The cahiers were official submissions of grievance and proposals for reform presented to Louis XVI by delegations from the Estates. The cahiers of the Clergy were overwhelmingly conservative and monarchical. But the Second Estate is remarkably liberal, the vast majority willing to give up all financial privileges. Many cahiers from the nobility call for a written constitution and bill of rights. The cahier from Blois is representative of much opinion.

Deep and established ills cannot be cured with a single effort: the destruction of abuses is not the work of a day. Alas! Of what avail to reform them if their causes be not removed? The misfortune of France arises from the fact that it has never had a fixed constitution. [...]

This partition ought not to be otherwise than voluntary; in any other case the rights of property are violated: Hence it is the indefeasible and inalienable right of the nation to consent to its taxes.

So far from fighting tooth and nail for "feudal" privileges the nobility are often calling for reforms and the abolition of arbitrary privileges in favor of regular laws. They viewed the Estates General as an opportunity to establish a Constitution that would restrain the King's power and believed this would be done with the King's assent.

The reason is that in 1789 the nobility of France, especially in urban centers or important towns, is highly involved in commerce and stands to be more advantaged by reform of the government than preservation of increasingly irrelevant exemptions. It's no coincidence that the cahier of Blois's nobles recommends uniform measurements and reforms to customs taxes

Throughout the whole kingdom there should be but one code of laws, one system of weights and measures. That a commission be established composed of the most eminent, men of letters of the capital and provinces, and citizens of all orders, to formulate a plan of national education for the benefit of all classes of society; and for the purpose of revising elementary text-book. That all customs duties collected in the interior of the kingdom be abolished, and all custom-houses, offices and customs barriers be removed to the frontier.

The exceptions to the tendency of the Second Estate to promote reform are poor nobles dependent on small landholdings. In many of these cases the only real difference between a noble and a neighboring prosperous "peasant" are tax privileges, so this class aggressively defends privilege. There are relatively few of these however, particularly because these small nobles lack influence in any region where they are not the majority of the Second Estate.

My preferred introductory text for the French Revolution remains William Doyle's book, it would confirm my characterization.