How about this for an idea (Sanity check me please!).
Background:
In my TL the US is in the middle of the Great Depression (As per OTL) but Europe is better off than OTL (Mainly because they are 'Buying Europe' first and pumping up the economies of each other). The US is trying this with itself but it is not working too well (So result = OTL Depression). They see Europe and are jealous and this has upset the population, but politics do nothing.
Now as per my TL in 1935/36 there is a coup in Argentina and the Argentinans attack the Falkland Islands. They are retaken and the coup leaders overthrown by the British Empire following a land invasion. Argentina is restored as a soverign nation and the British Empire withdraws after trying those responsible and arranging new elections. US is pissed however and delcare it an breach of the Monroe Doctrine, and economically freeze UK assets etc. in the US. Response is a general cooling of relations between the US & UK, but nothing that time will not heal (As the UK has left Argentina by now).
This cooling trundles along for a few years and ends up in increased US / French relations (As France politically pissed at UK for various reasons). This in turn leads to increased US / Russia relations as well (As Russia friendly with France & Italy) - Side point however, as neither US or Russia really 'trust' each other and more than OTL. Just more trade).
Now, given this general cooling of US / Brit Empire relations, all you need is a few (Large) sparks or wildfires to get things worse politically. What if therefore a very minor situation indeed is seized upon and blown out of all proportion by the US press (Given the doom & gloom they would have been reporting, I believe that ANYTHING that diverts attention from their economy will be jumped upon!!). If this happens and the public become outraged by it (Again, easily possible I believe given the level of anger the population would have had about their economic position in the Great Depression), the politicans will NEED to issue some form of response to appease the public.
So, given this background what I am thinking is:
A minor situation and a few 'ill chosen' words spoken out of frustration (Related to each other) which when reported results in anger blown out of all proportion. This leads to a US military response (Overseas, maritime related incident so USN). The government knows things are blown out of proportion and send the ships more as a show of 'Look, we are doing something here' and expect things to be nothing more than an overseas training opportunity and to cool down in a few months. However what if an international incident occurs during this deployment and neither side (US / UK) then wish to back down? This will cause further cooling of relationships that other nations (Russia) can use to further divide the US / UK and this ultimatly leads to war (Something akin to a Russian staged "False Flag" oparation occurs to trigger actual declarations of war - Not planned in detail yet).
Is this possible?