Although a quick search of the Web draws up the speech, available here (with video and audio links), rare is the online news service that links to President Bush's remarks on May 1, 2003, aboard the USS Abraham Lincoln.
Since the media don't reprint excerpts of the speech nor give readers the links to the original source material, here are some comments from May 1, 2003, that point to President Bush warning Americans of an ongoing struggle to establish Iraqi democracy and counter the threat of terrorism (portions in bold are my emphasis):
We have difficult work to do in Iraq. We're bringing order to parts of that country that remain dangerous. We're pursuing and finding leaders of the old regime, who will be held to account for their crimes. We've begun the search for hidden chemical and biological weapons and already know of hundreds of sites that will be investigated. We're helping to rebuild Iraq, where the dictator built palaces for himself, instead of hospitals and schools. And we will stand with the new leaders of Iraq as they establish a government of, by, and for the Iraqi people. (Applause.)
The transition from dictatorship to democracy will take time, but it is worth every effort. Our coalition will stay until our work is done. Then we will leave, and we will leave behind a free Iraq. (Applause.)
Our mission continues. Al Qaeda is wounded, not destroyed. The scattered cells of the terrorist network still operate in many nations, and we know from daily intelligence that they continue to plot against free people. The proliferation of deadly weapons remains a serious danger. The enemies of freedom are not idle, and neither are we. Our government has taken unprecedented measures to defend the homeland. And we will continue to hunt down the enemy before he can strike. (Applause.)
The war on terror is not over; yet it is not endless. We do not know the day of final victory, but we have seen the turning of the tide. No act of the terrorists will change our purpose, or weaken our resolve, or alter their fate. Their cause is lost. Free nations will press on to victory. (Applause.)