The Navy delayed deploying a carrier today to the Persian Gulf, ostensibly on budgetary grounds, due to the "Sequester" still looming over the Department of Defense.
There will now only be one carrier in the Gulf on station, although carriers can get there in about two weeks, assuming transit through usual routes either direction Pacific or Atlantic.
As to the particular impact of this non-deployment, it is certainly possible to fly heavy bombers from U.S. locations to Diego Garcia if one had to, and to aerially refuel them from host countries, as to formidable bombardment capabilities, if there was a reason to have to do that.
Still, it does lower military capabilities in the Gulf, because such bombers would not have as much fighter air cover.
Whether that affects deterrence or not is unknowable fundamentally, although it does point to the impact of cuts in the Department of Defense in general, raising an interesting question: If we cut Defense spending, do we become more reliant on nuclear weapons, and the associated nuclear deterrence, other things equal?
It would not be the first time that had happened, as for budgetary reasons, Eisenhower very explicitly relied heavily on nuclear deterrence, if his critics then pointed out as they would now that it suffered from one serious flaw: Credibility.
If one relies on deterrence, it is important that deterrence be credible. Conventional forces usually are more of what Glenn Snyder called "defense over deterrence," in the sense that conventional weapons, carrier battle groups included, are mainly oriented towards conducting military operations designed to defeat adversaries directly, rather than deterring them from acting because of fear of punishment, if there is overlap of course.
Having the carriers present is mainly about deterrence, if it is a deterrence driven by military capabilities to defeat military moves, rather than "merely" punish with consequences that are so painful that potential adversaries don't want to experience.
All lines get blurred of course, but it would seem that as we cut the budget for Defense, we would either by relying on nuclear weapons more, or be altering our long-standing treaty commitments more, especially in Europe, and with Japan and Korea, the latter rather important now as North Korea continues to prepare a test.
Of course you can't have everything, and when you are a nuclear armed state, you can rely more on people being wary of what Shelling called the "threat that leaves something to chance" as to attacking or probing interests, although the credibility issue does somewhat invite tests with extended deterrence too.
So, Defense will have to come down for reasons of long run economies, but just be careful too about what you ask for too as to how enthusiastically that is done, as you might be pennywise and poundfoolish.
National Defense is as the Common Defense, the first function of all governments, if of course what constitutes "defense" is intrinsically subjective in character, given the lack of a world governing order with exclusive enforcement powers that are universally accepted as legitimate in all cases of disputes between States.