I don't perceive Egypt, Jordan, Saudi Arabia or the emirates as having independent governments. They are the closest equivalents today of indirectly ruled but colonially subjugated states of the British Empire from which those states' rulerships, in more cases than not, descend without any anti-colonial interruption. There is not a serious threat that these states may strike out and become independent under their current rulerships, though maintaining their rulerships is marginally more difficult as US demands become more onerous and humiliating, or as the cost the US forces Iran and Syria to pay for their independence is perceived as less onerous, less frightening both to would-be challengers for power and to domestic defenders of the status quo.
Apparently though, these states are able, behind closed doors, to tell Americans that US prestige in the region is declining.
The briefers reported that there was a growing perception among Arab leaders that the U.S. was incapable of standing up to Israel, that CENTCOM's mostly Arab constituency was losing faith in American promises, that Israeli intransigence on the Israeli-Palestinian conflict was jeopardizing U.S. standing in the region, and that Mitchell himself was (as a senior Pentagon officer later bluntly described it) "too old, too slow...and too late."US strategy in the Middle East is not dominated by strategic considerations. US strategy in the region is dominated by the fact that the idea that there must be a Jewish state has a kind of mystical status among US decision makers. The military can defeat advocates for Israel's interests in matters such as breaking up Iraq or confronting Turkey, but there are limits to the degree to which any US politician can confront Israel.
The January Mullen briefing was unprecedented. No previous CENTCOM commander had ever expressed himself on what is essentially a political issue; which is why the briefers were careful to tell Mullen that their conclusions followed from a December 2009 tour of the region where, on Petraeus's instructions, they spoke to senior Arab leaders. "Everywhere they went, the message was pretty humbling," a Pentagon officer familiar with the briefing says. "America was not only viewed as weak, but its military posture in the region was eroding."
How much pressure the United States can apply to Israel is an interesting question I'll have to think about later. It is not exactly none. The US backed down on its demand for Israel to cease construction in the occupied territories, but did get some minor concessions. The United States can threaten, and could execute if the threat is ignored, the interception of Israeli jets flying toward Iran. (If Israel were not to be intercepted, and was to start a war between the United States and Iran, that would likely by the end cause permanent, and possibly fatal, damage to the relationship between the US and Israal.)
Do Arabs see the US as a declining power? Possibly. It is not a decline that the US cannot create a viable state for the Palestinians. Any state in the occupied territories either would be an unacceptably non-sovereign collection of Bantustans or would have the ability to threaten Israel. That has always been the case. As time passes, Iran is becoming a more credible and effective counter-weight for the United States. But Iran being a tangible threat to the US colonies in the region is at least a medium, if not long-term concern.
In practical terms, the United States is today in approximately the same position with respect to the colonies as it was ten years ago, and for the most part can expect to be in that position five and possibly ten years from now. These colonial dictators like dressing up and making dramatic statements but really not much is changing.