As support for the Iraq war continues to ebb–and, no, I don’t think reaction to the London bombing will much of an impact on that support, except perhaps in the very short run–let’s not forget how little support Bush has for what he’s doing on the economic front.
A recent report by Gallup, “Bush’s Economic Report Card Shows Little Progress“, notes the following:

Americans remain concerned about the economy, as more say they expect it to get worse than get better, and Bush’s economic approval rating stands at 41%, with 55% disapproving.
Gallup asks the public on a monthly basis if Bush’s economic policies are “helping the economy, not having much effect, or hurting the economy.” The trend line over the last five months shows consistently lackluster ratings. Slightly more than a third of Americans (36%) say Bush’s economic policies are hurting the economy. This percentage has remained fairly steady, with a high point of 40% in April. A similar percentage of Americans (37%) say the president’s policies are not having much of an effect. About one in every four Americans (24%), on the other hand, say the president’s policymaking has helped the economy, and this percentage has hovered within a five-point range since February.

So only about a quarter of the public (and just 16 percent of self-identified moderates) believe Bush’s economic policies are actually helping the country. That should make the economy another difficult issue for the Republican party in 2006. As Democracy Corps’ report on their recent poll puts it:

Iraq will certainly be an issue, but do not underestimate the power of the economy. Structurally, this economy is not producing enough jobs to seriously tighten the labor market or enough income and benefits for people to feel they are making gains. When asked whether this is economy is doing well (creating jobs, rising incomes and home ownership and moving in the right direction) or not doing well (jobs scarce, incomes stagnant and benefits cut), a large majority (60 percent) are very clear that this economy is not performing for people.

Ah, but how to translate this economic dissatisfaction into the political coin of the realm, actual votes on election day? That’s the difficult part and, in the last couple of elections, Democrats have had little success doing just that.
An easy answer is: new ideas on the economy. But, as Jonathan Chait usefully reminds us in his New Republic piece, “The Case Against New Ideas: Policies Aren’t What Matters in Politics“, Democrats don’t lack for ideas, many of them fairly new, and, in fact, Democrats’ ideas tend to more resemble real ideas (as opposed to slogans) and to be more carefully worked-out than those of their Republican opponents. Moreover, there is little evidence that voters actually pay much attention to detailed ideas, however new, about public policy.
So is there no ideas problem in the Democratic party? Depends on what you mean by “ideas”, as Mark Schmitt points out in an excellent post on his Decembrist blog. It may be true that voters pay little attention to the details of policy ideas, but they do pay attention to what parties generally stand for and where, in general, they propose to take the country. And they do pay attention to the results of parties’ policies once they are in office.
The Democrats could use new ideas, therefore, but:
1. Those ideas should sum up clearly and simply what the party stands for and where it proposes to take the country.
2. Those ideas should be few in number and easily reduced to a key principle or two that can be transmitted to voters–otherwise voters are unlikely to pay much attention.
3. Those ideas should actually work in practice, so that voters will see the benefits of having the party in office and reward it with additional electoral success.
If Democrats can produce ideas on the economy that meet these criteria, I think they have an excellent chance of capitalizing, both short-term and long-term, on voter dissatisfaction with Republican management of the economy.
Otherwise, not.