Rick Santorum is under growing pressure from the Republican establishment to pull out of the presidential race as Mitt Romney appears to be coasting to victory in Wisconsin and two other party primaries on Tuesday.

The latest polls give Romney a seven percentage point lead over Santorum in Wisconsin and even heftier likely victories in Maryland and the District of Columbia. Those wins are expected to give Romney more than half the delegates he needs for the nomination, leaving the other challengers – led by Santorum – trailing badly.

But Romney is not faring so well in the polls against Barack Obama, who has opened up a significant lead with a large shift in support to the president among women.

The Republican leadership is alarmed by Obama's strengthening support even with a rocky economy and widespread dissatisfaction over some of his policies, such as the healthcare legislation fought over in the supreme court last week. It wants to see an end to the internal party struggle over the nomination so that the presumed winner, Romney, can begin shifting his campaign against Obama.

In recent days, a number of leading Republicans have endorsed Romney, a sign that they believe the primary is effectively over. The Republican leader in the Senate, Mitch McConnell, said that Romney is likely to be the nominee and suggested that the other contenders should drop out in order to allow him to focus on challenging Obama.

"I think it's absolutely apparent that it's 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," McConnell told CNN.

But Santorum is vowing to fight on for now. On Monday he predicted he may "sneak in and have an upset" in Wisconsin.

Santorum said that the calls for him to quit showed that the party establishment still feels he is a threat to Romney. "I'm encouraged by all of this," he said. "We've got a lot of folks seemingly getting very, very nervous two days before the Wisconsin primary."

Michael Biundo, Santorum's campaign manager, told the New York Times that Romney's camp is concerned that he may not fare well in next month's primaries in some southern states. "The Romney campaign would love to close this out and take the ball home with them, because they know May is going to be a great month for us," he said.

Santorum faces his own challenge to win the primary in his home state of Pennsylvania on 24 April. If he were to lose that, it may force him to withdraw. "We feel very comfortable that the people there in the Republican primary know us," he told Fox News. However he conceded it is "not going to be easy".

There is still a possibility that between them, Santorum, Newt Gingrich and Ron Paul can amass enough delegates to deny Romney the nomination outright and give them a say over the selection of a candidate at the Republican convention in August.

Paul told Face the Nation on Sunday that he is staying in the race to influence the agenda. "The truth is I'm trying to save the Republican Party from themselves because they want perpetual wars, they don't care about presidents who assassinate American citizens, they don't care about searching our houses without a search warrant and these are the kind of things that people care about," he said.

While Romney is increasingly confident of the Republican nomination, the poll numbers are not good in his challenge to Obama. A USA Today/Gallup poll found that the president has taken a significant lead over Romney in the key election battleground states, in large part because of rising support among women.

Obama commands 51% support in the dozen top swing states, nine percentage points ahead of Romney. The poll showed that the biggest change in support was among women under 50 with the president commanding their support by two to one against Romney, in part likely a response to the recent battles over access to contraception on health insurance.