Robert Gibbs, the White House spokesman, said the president would do "whatever it takes to get healthcare done" and Obama said Americans were waiting for the administration to lead.
It now appears likely that Obama's fellow Democrats will use a congressional procedure called "reconciliation".
The process requires only a simple majority instead of the usual 60 votes that are needed in the 100-member chamber to overcome procedural hurdles.
The Democrats lost their "supermajority" of 60 votes after Republican Scott Brown won the Massachusetts seat left vacant by the death of Democrat Edward Kennedy in January.
Without "reconciliation", they would need at least one Republican senator's support for the healthcare measure – something they are unlikely to get.
Obama did not use the word reconciliation in his speech on Wednesday, but made clear he supported that process.
"No matter which approach you favour, I believe the United States congress owes the American people a final vote on healthcare reform," he said. "Now is the time to make a decision about how to finally reform healthcare so that it works."
Republicans dismissed Obama's comments and said Democrats risked paying a heavy price in mid-term congressional elections in November if they tried to push through the reforms without Republican support.
"Every election in America this fall will be a referendum on this issue," Mitch McConnell, the senate Republican leader, said.
Obama said his plan included ideas from his fellow Democrats as well as opposition Republicans, who staunchly oppose the idea of a large-scale overhaul of the $2.5 trillion healthcare industry, which accounts for one-sixth of the US economy.
Republicans say such a plan is too expensive for a government already running huge budget deficits.
Obama renewed his effort to win Republican backing with a healthcare summit last week and a letter on Tuesday outlining some of their ideas he was willing to adopt.
He said he was open to Republican ideas such as scrutinising healthcare providers who get federal money and offering more grants to study alternatives to medical malpractice suits.
Eleanor Clift, a contributing editor for Newsweek magazine, told Al Jazeera that since the Republican's victory in Massachusetts, "we've seen a different Obama - somebody who's willing to call out the Republicans for their obstructions and who understands that he has to rally the Democrats".
|Obama says another year of debate will not bridge the divide on healthcare [EPA]
"I think he thought that if you're rational and you explain to people what you're doing, that your good deeds will just speak for themselves, and he let his opponents define legislation that was emerging in a very negative way and he really didn't punch back," she said.
Now, however, "we're seeing a new aggressiveness and assertiveness".
Obama is due to travel to Philadelphia and St Louis next week to make his case for the healthcare overhaul, knowing full well that the political stakes are enormous.
Obama's approval ratings have dropped during the healthcare fight amid public worries about an unemployment rate hovering around 10 per cent.
With polls providing a mixed picture of their attitudes, the president made clear he was willing to let voters decide in November whether healthcare should be approved or not.
With more than one third of the senate and all seats in the House of Representatives up for grabs, his fellow Democrats want to move past healthcare to focus on job creation and the economy.
It is unclear whether Nancy Pelosi, the speaker of the House, will be able to muster a bare majority of 216 Democrats to pass the plan in the House, with moderates fearing a rebellion from voters more concerned about jobs.
But Clift told Al Jazeera that she thinks the plan will pass "because this is now the president's bill".
"Members of congress who are wavering will now have to go to the Oval Office and explain to the president why they're not backing him in an election year where Democrats are vulnerable.
"The president's put his imprint on it and I think he's made it pretty clear that the success of his presidency really hinges on him getting legislation."