In a speech marking his primary wins in Michigan and Arizona, U.S. Republican presidential hopeful Mitt Romney has promised to get Americans the oil from Canada "that we deserve."

Romney claimed a substantial win over his nearest rival Rick Santorum in Arizona Tuesday, securing nearly double the votes of his nearest rival there.

It was a different story in the state where Romney was born and raised, however. He just barely averted disaster with an unofficial 41 per cent of the vote, a scant 3 percentage points ahead of Santorum.

Acknowledging the narrow margin, the former Massachusetts governor told a crowd of supporters in Novi, Michigan that a win's a win.

"We didn't win by a lot, but we won by enough and that's all that counts," Romney said.

Reporting from Washington, CTV's Paul Workman said the results have failed to settle the major outstanding question about Romney's run for the Republican presidential nomination.

"The lingering question is: Does this get rid of all those doubts among many Republicans that he has the right stuff to beat Obama in November? And I would say, no it does not," Workman told CTV's Canada AM Wednesday morning.

In that context, Romney's victory speech Tuesday night largely ignored his Republican rivals to take direct aim at U.S. President Barack Obama instead.

Painting himself in stark contrast to the president, Romney said he would shrink government, repeal 'Obamacare', balance the budget and restore America's AAA credit rating if he's elected to the White House.

The crowd offered a relatively muted response until Romney touched on Obama's denial of a permit for a pipeline to carry bitumen from Alberta's oilsands to refineries on the U.S. Gulf Coast.

"He rejected the Keystone Pipeline," Romney said, pausing for a chorus of jeers from the audience before adding: "I'll get us that oil from Canada that we deserve.

"And by the way I'm going to open up our lands for development so we can finally get the energy in this country that we need at a price we can afford."

In January, the Obama administration denied Transcanada's application to construct the $7.6B pipeline through 6 states, citing a congressionally imposed deadline as providing insufficient time to assess the route. The company was invited to reapply, and has since said it now hopes the project will get underway by early 2015.

For his part, Santorum has said if he's elected president, he would also approve the pipeline "on day one."

Santorum, who won a trio of Midwest nominating contests in Missouri, Colorado and Minnesota on Feb. 7, had hoped to ride that momentum to victory on Tuesday. Instead, the former Pennsylvania senator will have to settle for a share of the delegates as Romney now heads into the run up to the 10-state "Super Tuesday" on March 6 as de facto frontrunner.

But in a press conference Tuesday -- his first media availability in three weeks -- Romney predicted more fierce primary fights to come.

"This is not going to be over in a day or two," he said. "This is a race to get the delegates I need to become our nominee ... In the final analysis, I anticipate being the nominee."