As Ms. Cheney arrived in New York with her father yesterday for the Republican convention -- a traditional showcase for candidates' adoring families -- her role in her father's campaign is becoming a subject of intense speculation on both sides of the same-sex marriage debate. Some on each side contend that the campaign is using her presence and Mr. Cheney's comments to soften its image and appeal to moderate voters at a time when the nation's attention is focused on the convention.