Is “Give (get) space” a common usage for “give (get) flexibility / freedom”?

NSNBC (March 26) reported that President Obama was overheard telling Russian President Dmitry Medvedev to “give him space" until after November during his meetings in South Korea on missile defense, and Time magazine (March 26) called Obama’s ‘Space’ Case “Gaffe of the Week.”

ABC news reported:

At his 90 minute meeting with Russian President Dmitri Medvedev Monday, President Obama said that he would have “more flexibility” to deal with controversial issues such as missile.

I have once heard “have elbow room” used to mean have freedom / flexibility of action (decision).

Is “give (get) space” commonly used as the equivalent to “give (get) flexibility”?

Give [someone] (some) space (see definition 19 in the link) is a common metaphor referring to a physical drawing away from the person in order for him/her to move freely. This can be used either in the context of giving someone privacy when they are grieving/hurt, or in the context of getting out of the way while someone works (as in your example). Get some space is significantly less common as an idiom.

Give/have elbowroom is also a common idiom, useful either literally or metaphorically; however, it always has a connotation of giving someone freedom/flexibility to work, not of giving them privacy.

Cut [someone] some slack (mentioned by FumbleFingers in the comments) is a similar idiom to give [someone] elbowroom, and it, too, is not used in a context involving privacy. It tends to be applied in cases where the person is appreciably under your influence or authority, though it can be used by people on equal terms with one another.