By 72 percent to 23 percent, Americans broadly support President Barack Obama’s Afghanistan pullout plan, even though fewer than half agree with specific troop reduction goals, according to a Gallup poll released today.

The poll comes a week after the president’s announcement that he plans to withdraw 10,000 troops by the end of the year and another 20,000 or so by September 2012, at which point withdrawal would continue at an unspecified rate until 2014.

While, in general, those polled approve of that plan, the 30,000 number drew mixed reactions:

The slight majority of Democrats, 57%, say the 30,000 figure is about right; however — in line with vocal criticism of the plan from Rep. Nancy Pelosi and other congressional Democrats who want a more aggressive drawdown — 30% call it too low.

Independents’ reactions are more closely divided: 40% call it about right, 33% too low, and 18% too high. Republicans are the most fractured of all, with about a third saying the withdrawal figure is about right, a third calling it too high, and 20% too low.

Similarly, even though voters agree the United States should begin to withdraw now, they’re still divided about whether an official — and announced — timetable is a good idea.

Americans’ reaction to Obama’s timetable for withdrawing troops could reflect their views on the pace of troop withdrawal as well as their perceptions about the impact that announcing a timetable could have on the U.S. war effort. Perhaps as a result, less than a third (30%) roundly endorse Obama’s timetable, while another third think the troops should be withdrawn sooner and 31% think the U.S. should not set any timetable.

Democrats are the most supportive of the timetable, but not even a majority of Democrats agree with it — just 45 percent. (But that’s because 40 percent prefer an accelerated version.) A slight majority of Republicans — 54 percent — say no timetable should be set in the first place.

Disapproval of the precise timetable aside, the president’s plan is working in just the way he most wanted and needed it to: It’s helping his reelection campaign. For that cause, the president will jeopardize recent successes in Afghanistan. For that cause, he’ll “signal to allies and enemies alike that the United States is more committed to extricating itself from the fight than it is to ensuring that stability in the region is achieved,” as The Heritage Foundation’s Mike Brownfield put it. For that cause, his administration will even lie about Gen. David Petraeus’ withdrawal recommendations. Anything to win the electorate’s approval.