5.2.4 Final US Card. In any US Action Phase that the US side is holding only one card, it may play it, discard it (without effect), or hold it.
If in US Action Phase 1 the US holds 2 cards and the Jihaddist holds 3 cards (due to Quagmire for instance) the US must play one card and (as stated ) elect to play the second, discard it without triggering any effects or hold it. Action goes back to Jihaddist for Action Phase 1 and Action Phase 2 (1 card left in Jihaddists Hand).
US may again play its last card (if they held and didn't lose it), discard it without effect or hold onto it.
Action back to Jihaddist for his last card to play.
And a final decision for the US (same as above), whatever they decide, the turn ends after that Action Phase.
Either by playing/discarding of last card as of
5.2.1 [...] A Turn ends and a new Turn begins when each side has expended the cards it was dealt[...]
or by holding it to the next turn.
5.2.4 Final US Card. [...]If the Jihadist side has expended its cards and the US side holds its final card, resolve any plots and end the turn.
5.2.3 Unblocked Plots. At the end of each US Action Phase (whether or not the US played any cards), resolve all Plots in any countries (8.5.6).