Get resources inside or outside constructor?
Are these resources always linked to the bigObject instance? Do they have something in common with certain data or functionality in bigObject? Are they somehow related mutually? It's hard to say exactly what is the better approach without knowing all this, but there are several sanity checks you can do:


Do GetResource1 to GetResource3 really all depend on the bigObject instance? Can you extract this functionality into a different class? Extract class refactoring might be an option.
Does bigObject know too much? Big kinda sounds like God, as in "god object".
If these three resources always come together (i.e. they all belong to the same interface), you might want to extract only them into a "parameter object". This means that you might end up with something in the middle, like:

public Foo(Bar bigObject, IResources resources)
{
   ...
}


Which means your bigObject will implement IResources, but you will also be able to implement them in a different way, and it will reduce the number of params.
If these resources are all of the same type, and there is a large number of them, then even a simple delegate might be enough. You might even want to make the call weakly typed for greater extensibility:

public Foo(Bar bigObject, Func&lt;string, IRes&gt; getResourceByName)
{
     var res1 = getResourceByName("1");
     var res2 = getResourceByName("2");
     ...
}



These suggestions popped out as I was writing, but ultimately, it's hard to give any exact guidance unless you state the actual problem you are trying to solve. Design should then follow from there.