(CNN) -- Some leading social conservative groups are praising Rick Santorum following his suspension of his Republican presidential campaign. But their reaction Tuesday didn't mention Mitt Romney, the all-but-certain GOP nominee with Santorum out of the race.
That could spell trouble for Romney as he tries now tries to consolidate the Republican base by reaching out to the social conservative voters who backed Santorum and other candidates during the long and divisive battle for the nomination.
"Rick Santorum's historic run for president achieved remarkable success because his campaign was based not on money spent, but on the message of faith, family and freedom that he carried. I commend his courage, boldness and tenacity in fighting for the values that made America great, and are fundamental to returning America to greatness," said Tony Perkins, president of the Family Research Council Action, a leading social conservative group.
"Millions of voters flocked to Rick not because he was a Republican, but because he passionately articulated the connection between America's financial greatness and its moral and cultural wholeness. He realizes that real problem-solving starts with an understanding that the economy and the family are indivisible.
The statement didn't mention Romney.
Neither did a statement by Susan B. Anthony List, another leading social conservative group.
"With great vision and passion, Rick Santorum reached the hearts of pro-life voters and allowed them to show the strength of their voting bloc," said Marjorie Dannenfelser, president of SBA List. "The Susan B. Anthony List is proud to have mobilized those key voters."
"Pro-life voters are a consistent and growing constituency, who proved invaluable to Senator Santorum in state after state throughout the primary elections. We will continue to reach out and mobilize those voters and millions more like them across the country. The political muscle of the pro-life movement will be critical to defeating President Obama in November." added Dannenfelser, who also didn't mention Romney by name.
Perkins was the spokesman of a January conference in which three-quarters of the social conservative leaders attending endorsed Santorum's bid for the nomination.
Social conservative voters, who are a crucial part of the GOP base, were the backbone of Santorum's campaign. They flocked to him for his longtime stance against abortion rights and same-sex marriage, and for his personal story of being a devout Catholic who home-schooled his seven children.
Thanks to their support, the former senator from Pennsylvania went from a long shot last year to the top of the pack in February. According to exit polls, Santorum came out on top in states where self-described born-again Christians made up a majority of the GOP primary electorate.
With Santorum gone, the big question is whether social conservatives will now support Romney -- or if they'll sit out the presidential election come November and concentrate their efforts down ballot in the Senate and House races.
In an interview with CNN senior congressional correspondent Dana Bash, Perkins said that conservative activists are so unenthusiastic about Romney that many are likely turn their grassroots efforts away from the presidential race and towards Congress -- specifically putting the Senate in Republican hands.
"It's difficult for us to back a candidate our constituents don't believe in and aren't excited about," Perkins said in a telephone interview, speaking about Romney.
Perkins also told Bash that the consensus was to turn their "emphasis" to campaigns for Congress rather than campaign for Romney.
Evangelical activist Michael Farris was not exactly surprised that Rick Santorum suspended his campaign on Tuesday. But that doesn't mean that Farris, a longtime political organizer, knows what he's supposed to do now.
"Right now my choice is to sit on my hands and do nothing or to actively try to find some alternative" to Mitt Romney, Farris told CNN.com Religion Editor Dan Gilgoff, soon after Santorum's announcement.
"Some of us just have a hard time supporting a person who said he was going to be more liberal on gay rights than Ted Kennedy," said Farris, chairman of the Home School Legal Defense Association, referring to remarks Romney made in a 1994 letter, during his unsuccessful Senate bid to try and unseat Kennedy.
Gilgoff says that Farris' reaction is "a stark emblem of the disappointment among religious conservatives over Santorum's announcement, and a reminder that Romney's enthusiasm deficit among the conservative evangelicals who form the GOP's base hasn't gone away."
But CNN senior political analyst Ron Brownstein says that in the end, social conservatives will close ranks around Romney.
"Mitt Romney will do fine among evangelical Christian voters who are very conservative on social and role of government issues, and he will probably win over 90% of Republican voters in the end mostly because whatever they think about Romney, they know they don't want Barack Obama in the White House for antoher term."
"This is now a team sport. Everyone knows what team they are on, and the vast majority support their team," adds Brownstein, editorial director at National Journal.