ST. PAUL, Minnesota (CNN) -- A group of gay and lesbian Republicans has traveled to the site of the GOP convention this week to help convince its party that it is time to stop being on the "wrong side" of the same-sex marriage issue.

Log Cabin Republicans President Patrick Sammon says "momentum is on our side."

"Clearly, the tide is turning," said Scott Tucker, communications director for the Log Cabin Republicans. "It's important for the Republican Party to be inclusive on this issue, because we are at risk of being on the wrong side of history."

Although the group's president, Patrick Sammon, acknowledges that few politicians in either party support "marriage equality," as the group dubs the same-sex marriage issue, "it's clear momentum is on our side."

Sammon and other Log Cabin Republicans pointed to a poll indicating that the party is starting to move closer to their positions.

A CBS News/New York Times poll released Monday found that 49 percent of the delegates to the Republican convention support allowing same-sex marriages or civil unions. The poll's margin of error is plus or minus 3 percentage points.

A CNN/Opinion Research Poll conducted in May found that nearly half of those surveyed supported either same-sex marriages or civil union. Twenty-four percent supported same-sex marriages, while 27 percent backed civil unions. Forty-three percent backed neither option. The poll's margin of error was plus or minus 3 percentage points.

Despite his opposition to same-sex marriage, the Log Cabin Republicans said they endorsed Sen. John McCain, the GOP's presumptive Republican presidential nominee, on Tuesday because he embraces an approach to politics they want their party to return to.

McCain is an "inclusive Republican who believes that our party needs to get back to our core unifying principles that lead us to victory in the '90s," Tucker said, noting that the Arizona Republican has had a long relationship with the Log Cabin Republicans.

"He's a very inclusive Republican, a different type of Republican," Sammon said "At the same time, we have honest disagreements on some issues."

In making its endorsement, the group pointed to the Arizona senator's opposition to a federal constitutional amendment that would have defined marriage as being a man and a woman. The amendment has strong support from social conservatives and would have reversed the decisions by Massachusetts, California and New Jersey to allow same-sex marriages.

"That took a lot courage for a senator from a red state to buck his own party," Tucker said.

Although McCain personally opposes same-sex marriage, he voted against the amendment, in part, because he believes the issues should be left to the states.

"John McCain stood up for us ... and I want to stand up for John McCain," said David Valkema, a director of a fine arts foundation in Chicago, Illinois. "He doesn't care about my sexuality. He cares that I am an American.

"He's teachable," Valkema added.

Despite her positions on gay rights issues being largely unknown, Sammon said, the Log Cabin Republicans were also satisfied with McCain's choice of running mate, Alaska Gov. Sarah Palin.

Unlike McCain, Palin has expressed support for the Federal Marriage Amendment, but Sammon said the group was comfortable with her being on the Republican ticket because of her 2006 decision to veto a bill that would have banned the state from providing benefits to same-sex partners of employees.

"She's a great choice," Valkema said. "We're learning more every day, but what we know, we like."

Although Palin was as blank slate for the Log Cabin Republicans, the group was extremely happy that McCain did not choose Mitt Romney, a former Massachusetts governor and presidential candidate who was often mentioned as being on McCain's short list of vice presidential choices, Tucker said.

While on the campaign trail, Romney often railed against his home state's decision to allow same-sex marriages.

"We would have had a problem ... if Sen. McCain would have chosen someone who used gay people as a wedge issue," Tucker said.

All About Same-Sex Marriage • Log Cabin Republicans • John McCain