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One day after a solid victory in New Hampshire, Republican presidential candidate Mitt Romney faces a critical test in South Carolina as he seeks to convince conservative voters that he is their best bet to defeat Democratic President Barack Obama.

Romney took a crucial step toward the Republican nomination on Tuesday with his win in New Hampshire, the second contest in the state-by-state battle for the Republican nomination. He won 39 percent of the vote and was well ahead of his nearest rival.

The former private equity executive also won the Iowa caucuses last week. He may now find it easier to convince skeptics within his own party that he is the strongest Republican to take on Obama in November's election, despite qualms about the moderate policies he pursued as Massachusetts governor.

Victory in South Carolina's Jan. 21 primary could derail rivals' hopes to consolidate a splintered conservative vote and set Romney on a steady march to nomination.

With economic concerns topping the agenda, Romney has argued that his experience as head of investment firm Bain Capital, where he made a personal fortune, would make him the best candidate to put the shaky U.S. economy on a stronger footing.

Romney gave perhaps the most dynamic speech of his campaign in Tuesday as he celebrated his victory in New Hampshire, outlining a stark contrast with Obama. Aides said it would set the tone for the rest of the campaign.

"We know that the future of this country is better than 8 or 9 percent unemployment. It is better than $15 trillion in debt. It is better than the misguided policies and broken promises of the last three years - and the failed leadership of one man," he said.

In recent days, rivals like former House of Representatives speaker Newt Gingrich have painted Romney as a heartless corporate raider who cut jobs in the companies he bought – an unusual debate in the business-friendly Republican Party. Influential conservatives like radio host Rush Limbaugh have warned that the attacks could undermine the party's free-market ideals.

Rivals could redouble their efforts in South Carolina, which has been hit hard by the economic downturn. Unemployment in the southern state stands at 9.9 percent, above the national average of 8.5 percent.

Texas Governor Rick Perry, who hopes to revive his fading campaign in South Carolina, has pointed to businesses in the state that were shuttered by Bain, while Gingrich allies plan to spend $3.4 million on ads criticizing Romney's business record.

Romney's Mormon faith was a stumbling block for some evangelical Christians in Iowa, who also make up a large percentage of the South Carolina electorate. Still, polls show Romney leading other candidates in the state.

A Reuters/Ipsos poll on Tuesday showed Romney was way ahead of rival Republicans nationally, with 30 percent support. He still trailed Obama by 5 percentage points in the White House race but was catching up.