Nope. The way the spring is retained in the post is that the butt end is flattened, giving it a taper, and then it's pushed into the hole in the post, pointy end first, and the taper is what holds it in the post. You remove it by taking it out the other direction. If you try to push it out in the direction it's installed, you'll either fail, or you'll succeed by ruining the hole from driving that hard steel taper through the soft brass. It HAS to come out in the OPPOSITE direction from the installation direction, in other words from the direction where the (now broken off) pointy end was.
Do NOT get phosphoric acid involved. If the thing's rusted in, what you need is penetrating oil.
But it's pretty likely that all you'll need is the pliers Pig S. pictured above, pushing the remaining bit out between the prongs of the slotted jaw. Once you get that taper started, it should pretty much fall out.