After a solid victory in New Hampshire, Mitt Romney looks toward a critical test in South Carolina next week as he seeks to convince conservative Republican voters he is their best bet to defeat Democratic President Barack Obama.

Romney took a giant step on Tuesday toward winning the state-by-state battle for the Republican presidential nomination as he captured 39 percent of the vote in New Hampshire's primary, following up his narrow victory in Iowa's caucuses a week earlier.

It's a good boost going into South Carolina, where I face an uphill climb, Romney said on MSNBC's Morning Joe program on Wednesday.

The former governor of neighboring Massachusetts, a one-time private equity executive, finished well ahead of his nearest rival despite facing sharp attacks calling him a heartless corporate raider who enjoyed cutting jobs at companies he bought.

He said he was ready to ward off the onslaught as he heads toward the next primary in South Carolina on January 21.

Take your best shot, Romney said to rivals. I've got President Obama coming next if I'm lucky enough to be the nominee.

Victory in South Carolina would essentially extinguish the Romney's rivals' hopes of consolidating a splintered conservative vote and stopping his march to the nomination.

Romney became the first Republican who is not an incumbent president to win both Iowa and New Hampshire. He may now find it easier to convince sceptics that he is the strongest Republican to take on Obama in November's election, despite qualms about moderate policies he pursued as Massachusetts governor.

The stumbling U.S. economy is expected to be the central issue of the 2012 campaign. Romney argues that his experience as head of investment firm Bain Capital, where he made a personal fortune estimated at some $250 million (162 million pounds), makes him the best candidate.

Romney took aim at Obama in his New Hampshire victory speech, which aides said 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.

OUTPACING RIVALS

In New Hampshire, Romney outpaced rivals Ron Paul, a U.S. congressman known for libertarian views, and Jon Huntsman, a moderate former U.S. ambassador to China and former governor of Utah who had focused his campaign on New Hampshire.

With nearly all precincts reporting, Paul was drawing about 23 percent and Huntsman 17 percent.

Newt Gingrich, a former speaker of the U.S. House of Representatives, and former Pennsylvania Senator Rick Santorum each received just over 9 percent of the votes.

Santorum's fifth-place finish in New Hampshire came just a week after he finished in a virtual tie for first in Iowa with Romney, who finished just eight votes ahead.

Santorum had campaigned hard in the midwestern state with an emphasis on social issues such as his opposition to gay marriage and abortion rights. Religious conservatives represent a much smaller part of the Republican base in New Hampshire, which has one of the lowest rates of church attendance and has legalized gay marriage.

In recent days, rivals like Gingrich and Santorum have lashed out at Romney for his record at Bain - 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.

South Carolina has been hit particularly hard by the economic downturn. The state's unemployment rate is 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. Gingrich allies plan to spend $3.4 million on ads there criticizing Romney's business record.

Romney's Mormon faith has also been 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 ahead in the state.

Surveys compiled by RealClearPolitics.com show Romney in first place in South Carolina with an average of 31.3 percent support, 10.6 percentage points ahead of Santorum, who was at 20.7 percent. Gingrich was just behind at 19.7 percent and Paul has 10.7 percent.

(Additional reporting by Susan Heavey and Vicki Allen in Washington, Editing by Patricia Zengerle and Eric Beech)