WASHINGTON — Elizabeth Warren did the convenient thing yesterday. She fell on her presidential sword, and took herself out of contention for 2016.

It’s highly probable that if she didn’t get her marching orders directly from President Obama or Hillary and Bill Clinton, then some intermediary made their desires known to her.

At the highest levels of the party, there is no desire for a Democratic primary bloodbath that would serve only the ?Republicans. Hillary Clinton sees 2016 as her year, and Obama, while personally closer to Warren, doesn’t want to run afoul of his own party’s most powerful couple in their quest to return to the White House.

It is possible, of course, that Warren arrived at this decision unbidden. It has, after all, been painfully clear that Hillary Clinton doesn’t want a Democratic version of the Tea Party — an idealistic progressive insurgency — emerging at her 2016 Democratic Convention.

Yesterday’s announcement by Warren that she’ll serve out her Senate term — which ends in 2018 — has to be sorely disappointing to the Republicans. Facing their own schisms, ?Republicans hoping for any shot at reclaiming the White House in 2016 salivated over the idea of a Democratic primary contest that would pit a political veteran with strong connections and deep pockets against a first-term senator with a populist message and a reputation for taking on Wall Street for the little guy. At the very least the winner would emerge from the battle battered and cash-depleted.

For now, anyway, both progressives and Republicans will have to dream of other things.

In recent months, Warren had became the favorite presidential dark horse among the Democratic Party’s left wing, weary of President Obama’s slow rightward shift and wary of Hillary Clinton’s corporate ties.

The recent speculation of a Warren presidential run surely presented its own challenges for Warren herself. On the one hand, she felt the pressure of ?being virtually enlisted by people who embraced her own progressive ideals: holding big banks accountable, protecting consumers, fighting for fair working wages and protecting students from crushing college debt.

Like Warren at times, the progressives have expressed impatience with the Obama White House and congressional lawmakers on both sides of the aisle. Their call for an alternative to Clinton must have been difficult for Warren to ignore.

But surely, so were the pol­itical forces of the Clintons and Obama, for whom a Warren presidential campaign would have been more than problem­atic. Because of Obama’s close ties to Warren, the powerful Clintons might have held him responsible for any damage she did. But Warren hasn’t been afraid to challenge Obama on points of policy, and it is unclear if his objections alone would keep her out of the race.

When it comes to the Clintons, of course, the stakes are higher. Did Warren ever have a chance of besting Hillary in a primary? Doubtful. She’d be a headache at best. And if Warren continued to leave the door open to a presidential run, she risked making a vengeful, powerful enemy who could make her pay for years to come in Washington and beyond.

But here’s the thing: In politics, never never means never. Even Hillary declared in 2010 that she wouldn’t run for president.

In 2005, no one thought that a newly elected U.S. senator from Illinois would become the next president.

It’s only 2013; anything can happen. Warren’s insistence yesterday that she’s out for 2016 got the heat off her, freeing her to fight her own Senate battles.

But it’s not like 2016 is going anywhere, and if a door opens, she’ll be ready to walk through it.