WASHINGTON (Reuters)—A combative President Barack Obama Monday sought to regain the initiative on overhauling the U.S. health care system after legislation slowed down in the U.S. Congress while he was abroad last week.

Key lawmakers Sunday said the legislation, President Obama's top priority, was unlikely to be passed by Congress by the time they go on their August vacation, amid a debate among Democrats over how to pay for its $1 trillion cost over 10 years.

A higher income tax on the wealthy was an option offered Friday by an influential House of Representatives Democratic lawmaker, but it drew skepticism.

President Obama, just back from a week-long trip to Europe and Africa, used a Rose Garden ceremony to make his case for the health care revamp and to tell his critics they should not write him off too soon on the subject.

"I just want to put everybody on notice, because there was a lot of chatter during the week that I was gone: We are going to get this done. Inaction is not an option."

"For those naysayers and cynics who think that this is not going to happen, don't bet against us. We are going to make this thing happen," he said.

Senate Majority Leader Harry Reid, D-Nev., said Monday the goal was unchanged. "We'd like to see these bills on the floor in July. And we hope our Republican colleagues will work with us to achieve that goal," he said on the Senate floor.

Some political commentators have raised questions about whether President Obama should get more directly involved in health care negotiations.

Committee leaders in the House of Representatives planned to introduce a health care overhaul measure Monday and consider amendments later in the week, even as they search for ways to fund the program.

Rep Charles Rangel, D-N.Y., head of the House Ways and Means Committee, said the bill would include a tax on Americans earning more than $350,000 per year that would raise $540 billion over 10 years. The tax would begin in 2011 and have higher rates at the $500,000 and $1 million income levels.

This higher tax is expected to be opposed in the Senate.

President Obama predicted more debate in the days ahead but said he would be successful in fulfilling his campaign pledge.

"Even though we are close, I've got no illusions that it's going to be easy to get over the finish line. There are going to be more debates and more disagreements before all is said and done, but health care reform must be done," President Obama said.

As the overhaul legislation moves through Congress, health insurers, drug companies and hospitals are under pressure to help control the rapidly rising cost of U.S. health care. U.S. health insurers were in talks with the Senate Finance Committee to reach savings in the Medicare program for the elderly and disabled of $100 billion over a decade, a source familiar with the talks said Monday. That follows the announcement of commitments for savings over ten years of $80 billion from the pharmaceutical industry and $155 billion from the hospital sector.

The insurers' discussions focus on subsidies for Medicare beneficiaries who get their coverage through private Medicare Advantage programs. These plans receive subsidies at a cost greater than through traditional government-run Medicare programs.