> First off, human population can't grow exponentially

In the long-term, no. In the short-to-medium term, yes. If we are talking about relatively small religious subcultures, numbering in the tens/hundreds of thousands, the idea that they might make it to many millions before hitting fundamental barriers to further population growth is not implausible. And going from tens/hundreds of thousands to many millions would have huge political consequences, especially if we are talking about communities with a history of bloc voting.

> Second, I'm not sure Orthodox Jews are that culturally homogenous.

Of course not – and I think my comment acknowledged that by speaking of Hasidic/Haredi. There is a great deal of internal diversity within ultra-Orthodox (as opposed to Modern Orthodox) Judaism. However, at the same time, the different groups cooperate with each other heavily, through organisations such as Agudath Israel, Central Rabbinical Congress, Edah HaChareidis, etc. There is frequent intermarriage between them–indeed, it is the norm for marriages to be arranged between the children of the leaders of the different Hasidic dynasties. Their internal cultural differences are, by and large, not an obstacle to political cooperation between them in North America, when it comes to domestic political issues such as education, zoning and development, etc.

Most ultra-Orthodox Jews believe that the modern-day State of Israel is a sinful attempt to pre-empt the Messiah; but, they disagree on whether accepting Israeli government payments or voting or standing for election to the Knesset makes one sinfully complicit in that sin. These different attitudes towards the Israeli state are a major obstacle to the cooperation between the different groups in Israel; but that is a very Israel-specific issue, it doesn't impact their political cooperation in North America – especially since ultra-Orthodox Jewish political lobbying in the US focuses on practical domestic issues and (unlike other streams of American Judaism) is rather disinterested in foreign policy issues such as relations with Israel and the Middle East.

So, I doubt their internal cultural differences would be an obstacle to the scenario I'm suggesting.

> It is probably further obscured by solidarity and voting as a bloc, meaning agreeing ahead of time privately to present a united front to outsiders.

Of course they disagree among themselves on a lot of things, such as details of Jewish religious law – but those differences have little political relevance. They don't believe in using the government to force other (Orthodox) Jewish groups (or non-Jews) to follow their particular interpretation of Jewish religious law. They would, however, likely support the government forcing people to follow generically socially conservative mores (not fundamentally different from those espoused by conservative Christians and Muslims)–bans on abortion and pornography, anti-LGBT measures, etc

> And, if Israel is not the only Jewish state, it would be similar to the past. There were two in the past, Kingdom of Judea and Kingdom of Israel.

I think a fundamental difference is that those two kingdoms used to be one kingdom, which then split in two, and even then they were bordering on each other. By contrast, my hypothetical ultra-Orthodox Jewish state in North America would be a long way from Israel, would have a very different history, and a rather different culture and politics too–among other things, its dominant language would be Yiddish not Modern Hebrew. (That's putting aside the thorny historical debates about whether those two ancient kingdoms really existed or are legendary; and whether or not it is anachronistic to call them "Jewish".)