IOWA CITY, Iowa (Reuters) - President Barack Obama dared Republicans on Thursday to try to repeal his newly signed healthcare law but warned their effort would backfire as he touted the benefits of the massive overhaul.

President Barack Obama signs the health insurance reform bill during a ceremony in the East Room of the White House in Washington, March 23, 2010. REUTERS/Jason Reed

“If they want to have that fight, we can have it,” Obama told a university crowd in Iowa two days after putting his name on the most sweeping change in U.S. social policy in decades.

“I don’t believe the American people are going to put the insurance industry back in the driver’s seat. We’ve been there already. We’re not going back,” he said.

Taking his public relations blitz on the road as he seeks to overcome public doubts, Obama held a campaign-style rally at the University of Iowa Field House in Iowa City.

In the face of opinion polls showing the American public divided about the healthcare law, Obama and fellow Democrats are mounting an aggressive effort to gain credit for passage of the overhaul and to put Republicans on the defensive.

Obama first announced his healthcare plan in Iowa City in May 2007, launching a drive that aides say led to the bill passed by the House of Representatives and signed into law this week.

Republicans, who unanimously opposed the bill, have vowed to make repealing it a major issue in congressional elections in November.

“Well, I say go for it,” Obama said, goading his critics. “If these congressmen in Washington want to come here to Iowa and tell small business owners that they plan to take away their tax credits and essentially raise their taxes, be my guest.”

Designed to revamp the $2.5 trillion U.S. healthcare industry, which accounts for one-sixth of the country’s economy, the law will extend health insurance to 32 million Americans who lack it. It will bar practices like insurers’ refusing coverage to people with pre-existing medical conditions, expand the Medicaid government health insurance program for the poor and impose new taxes on the wealthy.

Obama acknowledged the bill was “not perfect” but listed what he saw as numerous benefits such as tax breaks to help Americans buy coverage.

‘BIRDS WERE CHIRPING’

Looking relaxed and upbeat, he mocked Republicans for acting as if the bill would lead to “Armageddon.”

“After I signed the bill, I looked around to see if there were any asteroids falling, some cracks opening up in the earth,” Obama said, adding it turned out to be a nice day and “birds were chirping, folks were strolling down the mall.”

Republicans are seeking to reduce or reverse Democrats’ big majorities in both houses of Congress in November’s elections.

The Senate on Thursday approved a package of final changes to the healthcare bill that must be approved again by the House after the Senate parliamentarian cut two minor provisions.

Speaking to reporters on Air Force One en route to Iowa, White House spokesman Robert Gibbs brushed aside complaints from two big manufacturers, Deere & Co and Caterpillar Inc, that healthcare reform would cost them hundreds of millions of dollars.

Gibbs said the healthcare law simply closed an accounting loophole that had been giving them a subsidy.

Support for the law seems to be growing, according to a poll released by Quinnipiac University on Thursday. Before the House passed the bill, 54 percent of Americans surveyed disapproved of it, while 36 percent supported it, the poll found. After the vote, the disapproval rating dropped to 49 percent versus 40 percent.