Is it in any way different from We should stop talking now? Of course the sentence structure is different, but do they imply the same thing?
This is a form of the subjunctive, where the ongoing action does not jibe with the required|wished-for action. To reflect this discrepancy between reality and requirement|wish, the tense shifts to the past, stopped. The time has come when we should not be talking.
In the US, we have both forms of this call-to-action: "It's time we stop talking, and take action..." and "It's time we stopped talking, and took action.". I think in England there's only the latter form (if Google ngram for time we stop talking is to be relied upon). The time we stop talking form seems to have had an interesting history in the US, spiking in the early 1940s, then fading away to nothing in the 1950s, and then spiking again in the 1960s.
The hypothetical past indicative is used after "It's (high) time (that) ..." with present-time reference. It is indeed similar in meaning to "We should ...".