WASHINGTON (CNN) -- Republican front-runner John McCain fended off former Arkansas Gov. Mike Huckabee in Virginia's presidential primary Tuesday and cruised to wins the other two "Potomac Primaries," but exit polls show the party's conservative core remains cool to the Arizona senator.
Three quarters of Republican voters polled Tuesday said they would be "satisfied" with a John McCain nomination.
CNN has projected the Arizona senator will beat Huckabee and his remaining rival, Rep. Ron Paul of Texas, in Virginia, Maryland and the District of Columbia, adding to his already wide lead in delegates to the party's September nominating convention in Minneapolis.
He racked up large leads over Huckabee in the Washington suburbs of northern Virginia and in the counties around Richmond, the capital. But Huckabee's strong showing highlights McCain's ongoing struggle to win over the party's conservative base, which exit polls found made up two-thirds of Virginia GOP voters.
McCain drew the support of only 32 percent of conservatives, exit polls indicated. Self-described GOP moderates voted more than 2-to-1 for the Arizona senator, but they made up little more than a quarter of the electorate.
He did better among conservatives in Maryland, winning a 43 percent plurality among them, while capturing more than three-quarters of a larger share of moderate voters. And in his victory speech, he reached out to conservative voters by stressing small government and national security. Watch analysts break down the GOP results »
"We believe that Americans, not our detractors, and certainly not our enemies, are on the right side of history," he said. "We trust in the strength, industry and goodness of the American people. We don't believe that government has all the answers."
But despite the reservations of conservatives, three-quarters of Republican voters surveyed Tuesday told pollsters they would be satisfied with McCain as the party's standard-bearer in November. See which prominent conservatives oppose, support McCain »
Huckabee's projected losses come just days after he beat McCain in two out of three weekend contests, and he is challenging the results in the third. He told reporters Tuesday night that he would stay in the race despite the latest results, offering himself as "a solid, conservative, absolute pro-life candidate."
The ordained Baptist minister had strong support from evangelical Christians, who made up nearly half of Tuesday's turnout. About 66 percent of Huckabee voters described themselves as born-again or evangelical, compared to about a third of McCain voters.
McCain has been battered by the party's conservative activist base and by talk-radio hosts. More than half of Huckabee's Virginia supporters -- 56 percent -- said they were frequent listeners to talk radio, compared to just 32 percent of McCain supporters.
After former Massachusetts Gov. Mitt Romney -- who had campaigned as the conservative alternative to McCain -- dropped out of the race last week, McCain tried to reassure conservative activists with a speech to their annual conference in Washington, promising to consult them on major decisions if elected president.
"You have a lot of social-based conservatives who want to make sure their voice is heard," GOP strategist Leslie Sanchez said. "They want to put pressure on McCain to make him clarify his position on things that are very crucial to them."
Virginia has been a GOP bastion in presidential races since 1968. But it has trended Democratic in recent state contests, with back-to-back Democratic governors and a Democratic senator, Jim Webb, elected in 2006.
Election officials reported higher-than-normal turnout for a primary, with 30 to 40 percent of registered voters casting ballots. High turnout was reported in the northern part of the state, which includes the Washington suburbs, and in the central part of the state, which includes the capital Richmond and the college town of Charlottesville.
In the days since Romney's departure, Huckabee won the Republican primary in Louisiana and the GOP caucuses in Kansas -- and he narrowly trailed McCain in Washington's state caucuses, where the former Arkansas governor has said he will challenge the result.
Terry Jeffrey, editor of the conservative magazine Human Events, said Huckabee's candidacy "is performing a valuable service" for the Republicans by forcing McCain to more clearly commit to conservative causes.
"I believe in a general election, if McCain is positioned to the right on those issues -- particularly cultural issues and immigration -- he'll stand a better chance of winning the swing voters that help Republicans in a general election," Jeffrey told CNN.
But he is running far behind McCain in delegates to the party's nominating convention in Minneapolis, Minnesota, late this summer. CNN's most recent estimate gives 812 delegates to McCain, including 26 "unpledged" delegates, and 217 to Huckabee including three unpledged.
A total of 1,191 delegates are needed to clinch the party's nomination.
A total of 113 delegates were at stake Tuesday -- 60 in Virginia, 37 in Maryland and 16 in the District of Columbia.
In Maryland, exit polls found McCain beating Huckabee by nearly 2-to-1 among suburban voters, who made up about 80 percent of the turnout. GOP voters in Maryland are heavily concentrated in the northern suburbs of Washington and around Baltimore.
Huckabee ran well among blue-collar voters in Virginia, but McCain had a strong edge among the same demographic in Maryland. While Huckabee won a majority of evangelical Christians, they made up a smaller proportion of the turnout in Maryland than in Virginia -- less than a third, compared to nearly half in Virginia.
McCain had the edge over Huckabee on the economy -- voters' No. 1 concern, as in previous contests. But McCain's strong suit among Republicans was his potential as commander-in-chief, with 62 percent of Maryland voters preferring the onetime Vietnam War POW over Huckabee, a onetime Baptist pastor, on that question.
McCain voters said their most important quality in a candidate was someone who "says what he believes," followed by someone with extensive experience. But among Huckabee voters, more than 70 percent rated their top quality in a candidate as someone "who shares my values." E-mail to a friend