The White House said Wednesday that stimulus act spending finally has kicked into high gear and as of June 30 had grown the economy by up to 3.2 percent and created up to 3.6 million jobs.

The report, the fourth quarterly analysis from the White House, comes as President Obama is trying to rehabilitate the image of the embattled $862 billion spending bill.

“The Recovery Act has played a key role in the turnaround of the economy that has been occurring over the past year,” the White House Council of Economic Advisors said in the report.

Republicans argue that the economy is still sluggish and that the stimulus has failed to meet even the administration’s original goals.

Before the law passed, the White House said unemployment would peak at 8 percent if Congress passed the stimulus. Instead, it rose past 10 percent and now stands at 9.5 percent.

Meanwhile, polls show voters don’t credit the stimulus with helping much.

Trying to turn those perceptions around, the administration is engaged in a summer-long effort to highlight projects being funded by the Recovery Act. On Thursday Mr. Obama will travel to Holland, Mich., for groundbreaking of a new plant that will build batteries for electric vehicles.

The report says that as of June 30, $480.3 billion had been either paid out in spending or allocated as tax cuts.

Of the 3.6 million jobs the White House says were created, just 800,000 of them are from public works projects such as building roads and bridges. The report says $86 billion has been spent on those projects, which works out to about $107,500 per job.

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