What does "radical pressures authored by Baghdad" mean?
As far as I can tell, no country in the Middle East other than Israel actually fears Iraq. Iran fought Iraq to a draw back in the '80s, when Iraq was supported by the Reagan administration. Kuwait is now well protected by US and UK forces. Saudi Arabia has sufficient air power to demolish any Iraqi attack. Syria has had friendly relations with Iraq, a similar Baathist tradition, and roughly equivalent military power. Turkey has greater military power. Jordan, like Kuwait is still functionally a UK/US protectorate.
They can't be terribly pleased that Saddam is building nukes, as well as chemical and bio weapons. His wanton destruction of the Kuwaiti oilfields upon withdrawing from Kuwait demonstrate a willingness to destroy for destruction's sake.
Saddam's weapons may be meant only for Israel, but nobody can be sure that some won't find its way into the radical terrorist organizations. In reality, there is nothing good that come out of Iraq's efforts to perfect weapons of mass destruction, even for Saudi Arabia.
The only reason we have a presence in the Middle East is because of Iraq. We weren't there to any extent before the Gulf War. Containment, as a strategy, has been successful in terms of protecting the region from Saddam so far, but it has been a total failure in terms of preventing the creation of WMD.
Why does Saddam want them so badly if he doesn't intend on using them for leverage, at a minimum, and to destroy entire populations, at worst?