About two dozen demonstrators on Monday stood just steps from the security perimeter outside the Republican National Convention (search) with a message unlike many others offered up by the large protest groups in New York City this week.

Carrying signs that suggest the open-party policy of the GOP is allowing abortion-rights supporters and other moderate voters to sway the party's direction, the atypical protesters outside Madison Square Garden argued that "a tent divided will not stand."

"Hasta La Vista Pro-Abort GOP," read one protester's sign. "Babies Die in Big Tent GOP" stated another. Demonstrators chanted: "Rudy Giuliani is a poison to the party."

The activists say they want the party to take a harder line on abortion and gay rights. They slammed the convention and its lineup of moderate speakers like California Gov. Arnold Schwarzenegger and former New York City Mayor Rudy Giuliani.

"Giuliani, [New York Gov. George] Pataki, Schwarzenegger. They're the poison to the party because they're not men of principle. They dishonor the party platform," said Randall Terry, founder of Operation Rescue (search) and president of the Society for Truth and Justice (search), both anti-abortion groups. "To parade them around is an act of deception and treachery."

Despite his harsh words for the Republican Party, Terry, who stood on the street corner organizing the small protest, said his beef is not with the president.

"Bush, thankfully, is pro-life, but for him [to allow these men to speak] in this year's convention is a grave mistake," he said.

Nationally, popular figures with appeal to Democrats and swing voters are headlining the convention's primetime lineups. Giuliani, New York Mayor Michael Bloomberg and Arizona Sen. John McCain (search) spoke on Monday. Schwarzenegger is on Tuesday's schedule, and Pataki is slated for Thursday. By contrast, more divisive and more conservative figures like House Majority Leader Tom Delay will be playing low-profile roles during the convention week.

Republican politicians and delegates say moderates are valuable in swaying swing voters, and dismiss the right-leaning protest by saying it is impossible to fully satisfy everyone

"You're going to see the broad base of our Republican Party," Bush-Cheney campaign spokesman Terry Holt told FOX News.

"We would not have become the dominant party without being a broader party," said former House Speaker Newt Gingrich (search), who defended the party's embrace and encouragement of the "big tent," despite his own conservative credentials. He insisted that conservatives and their more centrist brethren have more in common than most would think.

Speaking at an event sponsored by the moderate Main Street Partnership, Gingrich said he disagreed with groups like the influential Club for Growth, which has put millions into conservative Republican candidates challenging more moderate congressional incumbents.

Republicans on the other side of the security line added that they understood the party's position on moderates and argued that a swing to the right would alienate voters.

Bush is "very conservative" and understands that the party has "to do what is feasible" to appeal to conservatives and moderates, said Bob Bensing, a Pennsylvania delegate and chairman of the Ephrata Area Republican Committee, who describes himself as "on the right."

Bensing said he thought the vote in November would be a no-brainer for most conservatives.

"If you look at the two candidates and what they stand for, Bush is way out in front on conservative issues. … No one's going to suit everybody 100 percent, but you have to look at the total picture."

No convention will be embraced by everyone, said Sen. Lindsey Graham (search), R-S.C., a conservative who is on the speakers' list.

"If you want universal acceptance and agreement, you're going to have to move out of a democracy. Saddam Hussein won 100 percent of the vote," Graham said. "If we look at this as an opportunity to reach out and grow our number, it will be a huge success."

But Newsday Columnist Ellis Henican found fault with this strategy. "I'm starting to feel a little sorry for the real [Republicans]. The real guys, the ones who are going to govern, are not the ones the party wants to see."

The convention schedule certainly does not shut out conservatives. In addition to Vice President Dick Cheney, also on the schedule are prominent conservatives like Sens. Rick Santorum of Pennsylvania and Sam Brownback of Kansas.

Chris Slattery, also with the Society for Truth and Justice, said the group has planned protests at nearly two dozen events during convention week. Planned Parenthood's (search) "Stand-Up for Choice — Big Tent Republicans for Choice Extravaganza" and a Republicans for Choice fundraiser are among those events.

Although Slattery criticized the president's position on using existing stem cells for research, he primarily praised his record.

"Bush is our man. He's outstanding," Slattery said. But Slattery had unkind words about Cheney.

"We'd like to see Vice President Cheney keep his personal opinions on gay marriage to himself. He's got to stand behind the president," he said.

Despite his criticism of the GOP, Slattery noted that the next president is likely to make an appointment to a Supreme Court that is now divided on abortion rights, and was unequivocal about his choice in the November election.

"This is a life and death election for all the marbles: The most important election of the last 50 years," he said.