Image size limits?

If you were using OpenGL you could use:
int MaxTextureSize;
glGetIntegerv(GL_MAX_TEXTURE_SIZE, &MaxTextureSize);
And you will get the maximum height/width your texture can be on the current hardware.

Because you are using directx I imagine d3d has something similar, I am not sure but this could be the one you need:
http://msdn.microsof...s.90%29.aspx#Y0

Depends on your D3D version. If 9 you can use GetDeviceCaps and query the values of MaxTextureWidth and MaxTextureHeight. If you want to be sure of always being able to create a square texture, just take the lowest of these two values. D3D10 and 11 on the other hand guarantee a minimum maximum (!!!) texture size, which I believe is 8192 in the case of 10 and 16384 in the case of 11. Some hardware may go above this, of course.

You could also chunk the image into separate chunks and just render the chunks that are visible. It'll work on a lot of modern cards, but if you're targeting the average computer you could run into some problems creating a texture that size (the main problem lies in creating the texture, not necessarily just rendering it, though that itself can be a separate problem).

I got a warning in MSVS stating that some graphics cards can't support images that large.

Visual Studio gave you a warning about texture size? What exactly are we talking about, C++ and DirectX or C# and XNA or ... ?

I don't intend to display the entire image at once, instead the camera will pan around to allow the user to view sections of the image at a time. Would said graphics cards still have a problem with this?

This won't be of any importance. The device still must load and store the whole texture and the texture will be probably applied to some quad - whether you display only part of the quad doesn't matter at all.
As others said, you could split the texture to be sure it will be ok, for example instead of one quad with 4000x2500 texture you could have four quads each with 2000x1250.