A top congressional Republican has predicted Mitt Romney will be crowned as the party's presidential nominee, but the frontrunner's main rival Rick Santorum has vowed to fight on.
The White House also signalled that it sees Romney as the likely Republican challenger to President Barack Obama in November with Vice President Joe Biden attacking the former Massachusetts governor in a television interview.
Three months into a bitterly fought race for the nomination, Romney has a strong lead and polls suggest he will win three more primaries on Tuesday - in Wisconsin, Maryland and the US capital Washington.
"He's going to be an excellent candidate, and I think the chances are overwhelming that he will be our nominee," Mitch McConnell, the Republican leader in the senate, said Sunday.
"It seems to me we're in the final phases of wrapping up this nomination."
McConnell did not explicitly endorse Romney but suggested that the party should follow the lead of former president George W Bush and Congressman Paul Ryan, a leading Republican and representative for Wisconsin, who did.
"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," McConnell said on CNN's State of the Union.
The Real Clear Politics website poll had Romney, who has won 21 out of 34 nominating contests so far, leading Santorum 40% to 32.5% in Wisconsin.
But unless Romney can clinch the 1,144 delegates needed, he could be forced to wait until late August to get the nod.