Former Minnesota governor and candidate for the Republican 2012 nomination for president Tim Pawlenty speaks at the Cato Institute in Washington, D.C. on May 25, 2011. (Melina Mara / The Washington Post)

On Wednesday morning, former Minnesota governor Tim Pawlenty ambled onto the set of MSNBC’s “Morning Joe” and made some news, urging Republicans to “support reasonable increases to the minimum wage.”

Twitter was immediately ablaze, wondering why Pawlenty, a well-paid advocate for banks as chief executive of the Financial Services Roundtable, was backing wage hike -- a policy his lobbying group has not endorsed.

A couple of hours later, things escalated when Senate Majority Leader Harry Reid (D-Nev.) began his floor remarks by slyly invoking Pawlenty.

“I ask my colleagues to join us, join Governor Pawlenty,” Reid said.

Senate Republicans, however, did not, and at lunchtime voted nearly unanimously against opening debate on a bill to gradually raise the federal minimum wage to $10.10 an hour. One Republican, Sen. Bob Corker (Tenn.), voted aye.

But for Pawlenty, who briefly ran for president in 2011, the episode was a reminder that his brand of politics, often described as being for members of Sam’s Club rather than a country club, has few GOP enthusiasts.

In an interview late Wednesday, Pawlenty lamented the way his party is handling the ongoing debate on income inequality and warned that if it does not soon offer fresh proposals, it could face electoral trouble, especially in 2016.

“The issue has not yet risen to the level of attention it deserves, both inside and outside the party,” he said in a call from New York. “Republicans may benefit from near-term tailwinds this fall, but the demographic reality is that diverse voters have a diminishing view of Republicans and that needs to be addressed.”

“Elections are a marketplace,” he added. “The marketplace is telling Republicans that you need better products or marketing.”

Pawlenty said that while he does not support Reid’s minimum-wage bill, which he said goes “too far, too fast,” Republicans need to build an agenda that speaks to low-income Americans, with an emphasis on improving workers’ skills. “I personally believe that increasing the minimum wage should be part of a broader package,” he said.

On extending long-term unemployment insurance, another issue before Congress, Pawlenty said he would support “granting one more extension in a compromised form and agreeing that it’s the last one unless there is an economic downturn.”

In the House and Senate, Republicans have been reluctant to embrace such measures, and conservative groups have pressured Republicans to stay in line. With regard to engaging the poor, Republicans have been more active, with Sen. Rand Paul (R-Ky.) and Rep. Paul Ryan (R-Wis.) recently visiting urban areas.

As governor of deep-blue Minnesota, Pawlenty in 2005 signed an increase to the state’s minimum wage from $5.15 an hour to $6.15 an hour. He later vetoed an attempt to increase it again.

In the meantime, as Republicans mull whether to cut a deal, Pawlenty said party leaders should do more to highlight rising stars with blue-collar roots, such as Gov. Susana Martinez (N.M.) or Sen. Marco Rubio (Fla.).

“We need candidates and people whose faces look and sound and come from constituencies where we want to earn support,” he said. “We need our party’s leaders to be ready to pass the baton on to the next generation.”

“Look – my dad was a truck driver and my mom was a homemaker who died when I was young,” he said. “I have seen how important it is to help people get the education or the skills they need for the economy of today or tomorrow.”

When asked whether maybe he is looking to be a presidential contender again, perhaps running as a populist, Pawlenty firmly said, “no.” And asked whether he has received any negative feedback from financiers on Wednesday, his answer was the same.

But with one aside at Rockefeller Center, he did strike a nerve.