Atheist leader? In the US? As in the "most religious industrialized country in the world" US? NOT A CHANCE. In a country where a leader can not even support the separation of church and state (the foundation of any real democracy) without being accused of attacking religion, there is no chance whatsoever of anyone but a christian becoming president. Polls have shown that atheists are the most reviled community in America and have even indicated that many Americans would vote for a muslim (another group that is brutally discriminated against) before an atheist for the presidency. Lastly, I don't think a republican or democrat makes much difference to the equation as both "parties" are one half of the same coin and are MUCH more alike than different.
It will be a VERY long time before a professed Atheist from ANY party will ever win a nomination, much less the Presidency. Religious people in this country and others feel too strongly against those who are not religious to allow one to be President. Same thing with a professed Pagan.
A time will come when the first self-identified atheist Republican Presidential Candidate get close to or even win the nomination. In order for him to get close to or even win the nomination, he will have to show what he can do to his people.
As a christian, I don't think the people running for President that claim belief in God seem trustworthy. Even they just seem to be saying what they think we (I) want to hear and it's coming out badly. Everyone wants to find someone that's like minded and I don't see your wish coming to be for a long time.
It won't. Republicans are all about warping the Bible to promote the party. You won't find anyone in the Republican party nominated for such a high position who doesn't at least pretend to use the Bible to justify their warped morality.
Machiavelli stated in The Prince that, while fear of God can be replaced by fear of the prince, if there is a strong enough prince, Machiavelli felt that having a religion is especially essential to keeping a republic in order. For Machiavelli, a truly great prince can never be conventionally religious himself, but he should make his people religious if he can. According to Strauss (1958, pp. 226-227) he was not the first person to ever explain religion in this way, but his description of religion was novel because of the way he integrated this into his general account of princes. Thus, a strong leader must have the appearance of religion, but not possess it. True religion will weaken the strength of the leader, to Machiavelli. The Republican Party has historically had a strongly conservative/religious wing of the party, considered to be 40% of voting members (though a minority of the "establishment"). The party of atheism is the Democratic party; in fact, religious affiliation is the most predictive element in party affiliation. The exception to this is the Black Caucus; blacks have historically had close ties to church and church attendance, so the Democratic party stays close to Black churches while avoiding other churches. There is no history of an avowed atheist ever making it to a Republican nominee position at any time in the United States, and this is likely because atheists are, at most, 6% of the population in the USA, and are the least trusted "religion" in America as evidenced in repeated polls. They are a large part (polling 35-40%) of the Democrat party, but do not openly resonate within the Republican party.