Wisconsin Gov. Scott Walker during the North Carolina Republican Party convention in Raleigh, N.C., on June 5, 2015. (Gerry Broome/AP)

Wisconsin Gov. Scott Walker, who has been trying to bolster his conservative credentials as he eyes a run for the presidency, said Sunday that he would consider a constitutional amendment allowing states to ban same-sex marriage and that he "would not rule out boots on the ground" in Iraq.

"I personally believe that marriage is between one man and one woman," the Republican said on ABC's "This Week." But if the Supreme Court rules in favor of same-sex marriage across the country, he said, "the only next approach ... for those who are supporters of marriage being defined as between one man and one woman is, ultimately, to consider pursuing a constitutional amendment."

The decision on marriage should be left up to the states, he said.

Walker's comments came on a day when several Republican hopefuls tried to distinguish and introduce (or re-introduce) themselves to voters in a Republican primary field that is growing increasingly crowded and noisy.

Fresh off their announcements that they were jumping into the 2016 presidential race last week, Republican Sen. Lindsey Graham and former Texas governor Rick Perry cast themselves as down-home regular guys on the Sunday talk shows, defending their positions on voting rights and national defense while hitting on some of the main themes of their nascent candidacies.

[Scott Walker is the only potential presidential candidate who can go to a biker rally and mean it]

Graham, who announced his candidacy Monday in his home town of Central, S.C., showed why he is one of the most hawkish candidates in the party, saying on CNN's "State of the Union": "If you think we can protect America without some troops having to go back overseas and fight for a very long time most likely, then I am not your guy."

In the wake of a cyberattack on the Office of Personnel Management that potentially exposed the personal data of up to 4 million current and former federal workers, he called for more money to be spent to combat cyberterrorism.

"People in the intelligence community are more worried about this than anything else, a cyberattack on our country ... to knock the grid off, to get into our financial systems and basically shut down the financial services," he said.

Also appearing on CNN, Perry defended the voting identification law he signed — for which Democratic candidate Hillary Clinton has criticized him — saying that its purpose was not to discriminate against minority voters.

Perry said that the law was "overwhelmingly" supported by Texas voters and that it would stand up to a Supreme Court constitutional challenge should it come to that.

"I think we make it pretty easy in the state of Texas for people to vote," he said. "I don't know what her beef is with the people of the state of Texas about voter ID, but I think she is on the wrong side of the issue."

Former senator Rick Santorum (R-Pa.) cast himself as a champion for American workers, a theme that he said would guide his policies on immigration, the environment and taxes. When asked about the expectation that Pope Francis is expected to release a papal encyclical on the environment this summer, the Republican candidate said on "Fox News Sunday" that there "are more pressing problems confronting the Earth than climate change."

He continued, saying that "when it comes to me as someone who's trying to go out there and make sure we have a revitalization in manufacturing, to energy production, the things to create jobs and opportunities, that speculative science, which has proven over time not to have checked out, all the predictions that were made 15 years ago, none of them have come true."

Walker, who has not yet officially declared his intention to seek the Republican nomination, continued to sound very much like a candidate on Sunday, touting his record after he took part part in a “Roast and Ride” fundraiser for Sen. Joni Ernst (R-Iowa) this weekend.

Walker said his administration helped Wisconsin's unemployment rate drop from 8.1 percent to 4.4 percent, and he pledged to eventually hit a goal of creating 250,000 private-sector jobs.

He added that he wanted to "unleash the power" of the U.S. forces currently deployed in Iraq and wouldn't rule out sending more.