The strength of Obama's remarks are a clear indication that the White House has decided that the Republican frontrunner will be his party's presidential candidate and is not waiting for the primaries to run their course before going on the attack.
Romney is poised to seal his position as the Republican favourite on Tuesday with expected victories in primaries in Wisconsin, Maryland and Washington, DC, that will push him well past the half-way mark in the number of delegates required for the nomination.
Obama, in a speech in Washington, zeroed in on Romney's support for the Republican budget in the House of Representatives which proposes deep budget cuts the party says are necessary to combat the deficit. He called that justification "laughable" as he took a pointed stab at the parallel tax breaks for millionaires – an issue on which Romney is particularly vulnerable because of his estimated $220m fortune.
The president painted the Republicans as serving the rich over the middle class by proposing "more than a trillion dollars in tax giveaways for people making more than $250,000 a year".
"That's an average of at least $150,000 for every millionaire in this country," he said. "It is a Trojan horse disguised as deficit reduction plans. It is really an attempt to impose a radical vision on our country. It is thinly veiled social Darwinism. It is antithetical to our entire history as a land of opportunity."
Obama said that along with the tax breaks would come "massive new cuts in domestic spending" supported by Romney that would "pull up the ladder for the next generation". Benefits would be removed that had helped uplift millions of Americans. "I don't think people fully appreciate the nature of this budget," he said.
The president said that if the cuts were spread out evenly it would mean cuts in aid to millions of college students, the slashing of medical and scientific research grants and over 200,000 children losing early places in school. The department of justice would have less money to combat violent and financial crimes.
"Two million mothers and young children would be cut from a programme that gives them access to healthy food," he said. "We wouldn't have the capacity to enforce the laws that protect the air we breathe, the water we drink or the food that we eat.
"Republicans may say well we'll avoid some of these cuts, since they don't specify exactly the cuts they would make. But they can only avoid some of these cuts if they cut even deeper in other areas. This is math."
The president's stinging attack, at a lunch hosted by the Associated Press, came as Romney was expected to win at least two primaries on Tuesday night. If he sealed all three, it would ratchet up the pressure on his rivals to drop out of the race and allow the Republican party to concentrate on campaigning against Obama.
Romney faces his strongest challenge in Wisconsin. The former Massachusetts governor has pulled ahead of Rick Santorum ahead in recent opinion polls, but his lead remains in single digits. He has an apparently unassailable lead in Maryland of more than 15 percentage points and Santorum failed to collect enough signatures to get his name on the ballot in Washington, DC.
"I would like to win in Wisconsin and I think I will," Romney told a Milwaukee radio station. "I'm hoping for a big turnout. My experience is if we have a big turnout, particularly Republicans, I will do particularly well."
The Republican establishment has stepped up pressure on Santorum to quit the race. The Republican leader in the Senate, Mitch McConnell, said that it is in "the best interests of our party at this particular point to get behind the person who is obviously going to be our nominee and to begin to make the case against the president of the United States".
Santorum has vowed to stay in the race but the former Pennsylvania senator's stamina for continuing the fight may be weakened by an increasingly difficult contest in his home state which he must win to retain what remains of his credibility as a candidate.
A Quinnipiac University poll released on Tuesday shows that Santorum's lead over Romney has been cut in half to just six percentage points in the Pennsylvania primary later this month. Santorum has 41% support among Republican voters to Romney's 35%. The survey suggests that the momentum is with Romney, and it is only likely to pick up after Tuesday's primaries.
Another recent poll, by Franklin & Marshall College, showed the two candidates almost tied.
However, there was some good news for Santorum in the Quinnipiac poll in that 57% of voters agree that his remaining in the race will be good for the Republican party whereas 33% thought he should drop out.
Still, Santorum is worried enough to have abandoned campaigning in Wisconsin on election day to hit Pennsylvania.
Santorum has justified staying in the race by saying that Romney is a weak candidate by pointing to the low voter turnout in states won by the frontrunner. Santorum said that the votes of many of the delegates claimed by Romney are up for grabs if he does not win an outright majority.
"Now a huge percentage of the delegates are unbound," he said while campaigning in Wisconsin on Monday. "A majority would be unbound after the first ballot. It would be average activists, Republicans who run for delegates who are involved in the party."
