It would possibly be quite happy on a US dryer supply, although the 60hz is not really ideal
European machines are designed to run on 230V +/- 10% at 50Hz. (207 - 253V) They're also designed so that polarity is not an issue. i.e. the normal European grounded plug is fully invertable i.e. you can connect it either way. Thus, polarity is random.
Because of this, the machines are designed so that they function perfectly in either polarity. This means, that on a US supply with 2 hots, the machine should still function perfectly safely.
Just remember the colour code when fitting a US plug
EU code:
Blue - Neutral
Brown - Live/Hot
Green & Yellow striped cable - Ground (Earth)
It's worth noting that there are (or at least were until releatively recently) a few pockets in europe where you could still find supplies that provided 2 X 127V hots rather than 220V hot and a 0V neutral. The difference between those 2 hot cables was 220V.
Pre 1950s, some european countries had a mixture of 127V and 220V appliances, much the same as the US has now only at 50Hz. In the 1950s, everything was standardised to 220V 50Hz. In some older installations, this was achieved simply by installing new outlets and providing them all with 2 X hot wires. Thus, polarity didn't matter at all.
All appliances, including lamps etc, were designed to operate safely in this environment.
There was a further harmonisation in the early 1990s which is still on-going to bring the UK, Malta and Cyprus into line with the rest of Europe.
The UK, Malta and Cyprus used a slightly higher nominal voltage : 240V 50Hz
Rest of Europe (including the Rep. of Ireland) used 220V 50Hz
So, they set the EU-wide nominal voltage as 230V 50Hz and all appliances were manufactured to this specification.
220V and 240V supplies are within their designed tollerances.
However, EU supplies are being moved closer to 230V 50Hz.
It's more significant that the UK drops its voltage to 230V as 240V supplies when they peak / spike can go outside the 230V +/-10% range!! In general it has meant that surge protectors are a little more warrented in the UK, Malta and Cyprus than elsewhere in the EU. Although, in my experience, no where in Northern Europe has voltages as unstable as I have noticed in parts of North America. We had regular brownouts and spikes in urban Boston that toasted some IT equipment. I have never experienced anything like that in Europe.
The only problem I think you could have in the US is that the supplies in your homes are 240V and I am not sure what the allowed range of voltages is i.e. you could end up with a peak voltage of >250V which could be outside the tollerance of a normal European appliance and could damage sensitive circuitry.
You could end up shortening the life of the appliance, particularly the programmer.