I've seen a few comments to the effect of, "why write the President about this? It's Congress that funds things." Which is technically true, but ignores a lot of important stuff about the process.
First off, any message sent through our form to contact the President is also sent to your elected officials in Congress. So there's that.
But back to the President, how does he fit into this process?
Well, right now we're worrying about two fiscal years: the one that started in October – FY2014 – and the one starting next October, FY2015. Congress is hammering out their issues with FY2104 (remember the shutdown?) and a budget committee is set to do something by December 15th. The temporary funding for this year expires in January, and we want to make sure that they don't forget about planetary exploration. Both the Senate and the House have proposed legislation that funds Planetary Science at $1.3 billion, which is about $100 million more than the White House requested.
The other budget that we're worried about is FY2015. At the moment, this budget is embargoed by the White House as they finish drafting it. This budget request will come out sometime in the early spring and even though the President doesn't then actually fund anything, it does represent official Administration policy, the tune of which NASA marches to.
Unless the program is particularly political – health care, say – the funding levels proposed by the White House tend to act as a cognitive anchor and Congress usually doesn't stray too far from the initial numbers. You're in a much better position if a program has strong White House support that is reflected through the first budget request.
It's also the Administration that puts in formal requests for "new starts" of bigger projects. Do you want to see a mission to explore Europa? I do. But it requires NASA, the Office of Management and Budget, and the White House to all support it in order to put it in their budget. Congress can then approve the funding, but since Congress only works on a year-to-year basis, they can't initiate a major, decade-long project.
Until the White House decides to prioritize Planetary Science, we'll likely see this same story. Every year, the White House will propose cutting Planetary Science. The public, scientists, and organizations like the Planetary Society will work really hard to get people in Congress to restore funding. That's not sustainable until the White House changes its tune.