IOWA CITY, Iowa - President Barack Obama mocked Republicans' campaign to repeal his new health care law, saying they should "Go for it" and see how well they fare with voters.

"Be my guest," Obama said Thursday in the first of many appearances around the country to sell the overhaul to voters before the fall congressional elections. "If they want to have that fight, we can have it. Because I don't believe the American people are going to put the insurance industry back in the driver's seat."

Obama's Iowa speech

With emotions raw around the nation over the party-line vote to approve the nearly $1 trillion, 10-year law, Obama took the opposition to task for "plenty of fear-mongering, plenty of overheated rhetoric."

"If you turn on the news, you'll see that those same folks are still shouting about how it's going to be the end of the world because this bill passed," said Obama, appearing before thousands in this college town where, as a presidential candidate three years ago, he first unveiled his health care proposals.

No Republican lawmakers voted for the overhaul, a sweeping package that will shape how almost every American will receive and pay for medical treatment. Many in the GOP are predicting it will prove devastating in November for the Democrats who voted for it.

But the president stressed the notion of a promise kept, saying the legislation he signed into law on Tuesday is evidence he will do as he said. As the crowd broke into a chant of "Yes we can!" Obama corrected them: "Yes we did!"

The White House suggests it has the upper hand against Republicans politically, arguing the GOP risks a voter backlash because a repeal would take away from small businesses and individuals the benefits provided to them immediately under the new law.

"We're not going back," Obama said.

Obama spoke as Democrats in Washington raced to complete the overhaul with a separate package of fixes to the main bill.

Senate leaders finished work Thursday on the fix-it legislation, already approved in the House. But Republican attempts to derail the process resulted in minor changes to the bill, which meant the House would have to vote on it again before it can go to Obama for his signature. The House vote was expected by evening.