Support for the U.S. plan to invade Iraq started out incredibly high in early 2002, but began to slip later in the year. However, overall support for an invasion to remove Saddam Hussein from power clearly increased after President George W. Bush's State of the Union Address and Secretary of State Colin Powell's presentation to the UN Security Council (see the UN Security Council and the Iraq war).
An early January 2003 poll showed rapidly decreasing support for an invasion, although there was still more public support than there was prior to the Gulf War a decade ago. Much of this appeared to be for the same reason that France and Germany oppose a war; namely the US public believing that the weapons inspectors should be given the time they need to complete their investigations. US officials downplayed this shift in public opinion, claiming that it is not a true reflection of the public mood.
A poll conducted at the time by The New York Times and CBS News released showed even less support for the US-led war. Approximately 2 out of 3 respondents wanted the government to wait for the UN inspections to end, and only 31% supported using military force immediately. Interestingly, this same poll showed that a majority of Americans believe that Iraq has weapons of mass destruction, but do not expect UN inspectors to find them. These numbers indicated a dramatic drop in support, as, two months prior, most polls showed about two-thirds of those polled supporting military action. However, about 60% of those polled do also support (at least in principle) the use of military action to remove Saddam from power, which closely mirrors recent polls taken by Time Magazine, CNN, FOX News, USA Today, CBS News and other news organizations. Recent polls also show that most Americans do not think that Saddam is cooperating with inspectors. 
Some polls showed that Bush's State of the Union increased US support for the invasion, but other polls showed that it had little effect. Most polls showed that support for the invasion, depending on how the question is phrased, at between 55-65% (58% according to CNN/USA Today, 57% according to the LA Times, and 67% according to Fox). However, the same polls also suggested that most Americans would still like to see more evidence against Iraq, and for UN weapons inspections to continue before making an invasion. For example, an ABC news poll reported than only 10% of Americans favored giving the inspectors less than a few weeks; 41% favored giving them a few weeks, 33% a few months, and 13% more than that. 
Some polls also showed that the majority of Americans believed that President Bush had made his case against Iraq. The Gallup poll, for example, found that 67% of those who watched the speech felt that the case had been made, which was a jump from 47% just prior the speech. However, many more Republicans than Democrats watched the speech, so this may not be an accurate reflection of the overall opinion of the American public. An ABC news poll found little difference in the percentage of Americans who felt that Bush has made his case for war after he had made his speech, with the percentage remaining at about 40%. 
Following Powell's February 5 speech at the UN, most polls, like one conducted by CNN and NBC, showed increased support for the invasion. NBC's Washington bureau chief Tim Russert, said the bumps in support were "largely" due to president Bush's State of the Union speech in January and to Powell's presentation on February 5, which most viewers felt offered strong evidence for action against Iraq. Bush's approval ratings jumped 7 points, and support for the invasion jumped 4 points. Only 27 percent opposed military action, the smallest percentage since the polls began in April of 2002. The percentage of Americans supporting an invasion without UN support jumped eight points to 37%. 49% of those polled felt that President Bush had prepared the country for war and its potential risks, a 9 point jump from the previous month.