I know that the visa waiver is being reconsidered but I'm not sure if anything has changed yet.
For those booking flights, until when can they be sure they'll be able to enter the EU without a visa?
(I'm assuming travel is with an American passport.)
There are two aspects to the question:
EU countries are extremely unlikely to put specific restrictions on entry by dual citizens. It's never been done nor discussed and would raise many questions. There is a general difference in philosophy at play here, US authorities routinely look at the country of birth for many purposes (e.g. security clearances) whereas European countries do not do that in the same way (being a citizen trumps everything else). It would not make sense as retaliation for the recent changes to the US visa waiver program either.
In any case, nothing has been announced and such a new rule would require an extensive rewriting of the Schengen regulations, which cannot happen overnight without anyone noticing, given the way the EU decision process works.
EU/Schengen countries are also very unlikely to put a blanket restriction on entry by all US citizens. This would in fact make sense as a retaliatory measure (or to protest other restrictions like the ESTA requirement or the fact that citizens from some EU countries are still not eligible for the VWP) and would be easier to implement (just a matter of removing the US from one list and adding it to another). But it would also jeopardize visa-free access to the US for all EU citizens and neither the treatement of Bulgarians, Poles and others nor that of dual Iranian-something citizens seem to be enough for other member states to take that risk.
Of course, that's not a certainty (what is in this area?) but until now the EU has only been able to complain a bit, with member states delaying any serious action and I feel fairly safe in predicting that it will continue that way. Case in point, the regulation cited by Tor-Einar Jarnbjo contains some pretty strong language but always had possibilities to delay actual restrictions pretty much indefinitely baked in and, sure enough, several ostensibly crucial deadlines have passed without any agreement to go beyond empty protestations.
Until when can they (US citizens) be sure they'll be able to enter the EU without a visa?
That is unfortunately impossible to say. If the EU decides to suspend visa free travel to the Schengen area for US citizens, the date of effect must be 'within 90 days' of the publication of the decision (Regulation (EU) No 1289/2013, Article 1(f)). It can neither be predicted if nor when the EU will make such a decision.
Excluding only dual US-Iranian citizens has not been a subject in the EU proceedings. The root issue is that the EU requires visa free travel for all EU citizens to a third country to allow citizens of the third country visa free travel to the Schengen area. Currently, citizens of Bulgaria, Croatia, Cyprus, Poland and Romania are not allowed visa-free travel to the US and these five member states notified the EU commision about the violation in 2014. After two years of negotiations between the EU and the US, no solution has been found and the next step would be for the EU to temporarily suspend visa free travel for US citizens to the Schengen area.
It has also been a subject in the discussions if the ESTA requirement is consistent with visa free travel. Even if an ESTA is not officially called a 'visa', it is a fee-based authorization for entry, which is required in advance and hence exhibits most of the characteristics of a visa.