He will do the same thing he did with the "red line" in Syria. He will fold.
He really doesnt have a choice but to fold though. Hagel has already stated Obama's plan to reduce military manpower back to pre WW2 levels. He has also come out and said we will no longer enjoy a military dominance under his leadership.
On a side note, I could actually go along with what Obama was doing if the cuts were left unspent and used to reduce deficits and debt. Its not though, he just plans on spending that money on expanded handout programs and "infrastructure" projects.