President Obama listens to an employee as he tours Michigan Biotechnology Institute during a visit to Lansing, Mich. (Kevin Lamarque/Reuters)

The warm-up act for President Obama’s speech here Friday featured a four-piece jazz band playing in front of a John Deere tractor. Obama’s quest to bring together two other disparate elements — Democrats and Republicans — was not as successful.

The president traveled to this middle-American college town to tout the passage of a $1 trillion farm bill this week, a rare bipartisan achievement by Congress that the president was eager to highlight. Six congressional Democrats flew aboard Air Force One — but none of the two dozen Republicans invited by Obama showed up.

House Agriculture Committee Chairman Frank D. Lucas (R-Okla.) “had other obligations,” explained one of his aides. House Speaker John A. Boehner (R-Ohio) was busy with his annual staff retreat. The only person to greet Obama at the airport was Lansing Mayor Virg Bernero (D), who shook the president’s hand in the bitter, below-zero-degree weather.

So the go-it-alone president carried on without them.

“This was a good sign Democrats and Republicans in Congress were able to come through with this bill and break the cycle of short-sighted, crisis-driven partisan decision-making,” Obama told a crowd of 500 at the McPhail Equine Performance Center on the Michigan State University campus. “That’s how we should expect Washington to work.”

Having pledged during his State of the Union address last month to more forcefully apply his executive authority to work around Republican opposition, Obama may have managed to make the problem even worse. Obama’s shifting tone — he’ll work with Congress when he feels like it and go around the legislative body when he wants — has led his rivals to wonder how they are supposed to trust him on the type of large-scale initiatives for which he needs their support, including immigration reform, long-term unemployment insurance and a minimum wage hike.

A day earlier, Boehner had dampened expectations for a bipartisan immigration deal by insisting that the GOP’s distrust of the president is too pronounced. Republicans have been attacking Obama for altering health-care law requirements, deferring deportations of young illegal immigrants and using his “pen and phone” — Obama’s phrase — to rule by “Executive Order tyranny.”

“He is running around the country telling everyone he’s going to keep acting on his own,” Boehner said. “And he’s feeding more distrust about whether he is committed to the rule of law.”

White House advisers said the president’s two-pronged approach does not contradict itself, and they said House Republicans’ long-standing opposition to Obama’s agenda means that he has no choice but to be more forceful.

At Michigan State, Obama announced a “made in rural America” initiative that aims to connect farmers with federal resources to help them sell their products abroad.

“Now, some of this opportunity agenda that I put forward will require congressional action, it’s true,” Obama said. “But as I said at the State of the Union, America does not stand still; neither will I. That’s why over the past two weeks I’ve taken steps, without legislation, without congressional action, to expand opportunity for more families.”

At the same time, the strategy has opened the president to charges that he is abusing his authority and skirting Congress. Republicans, looking ahead to this fall’s midterm elections, have taken advantage of the shift to paint the White House as insulated and overly political.

Asked about the GOP’s failure to be at Friday’s event, Sen. Debbie Stabenow (D-Mich.) said: “I wish they had been. As I understand it, a lot of them had conflicts. Whatever the reason was, we intend to celebrate.”

She said she was going out for ice cream with her grandchildren.

“People want us to get things done,” Stabenow said, dismissing a suggestion that Obama’s approach would further alienate House Republicans. “It’s way too partisan in Washington now, and there’s way too much gridlock. However we can move forward to solve problems, create jobs, get things done — that’s what we should be doing.”

Even as Obama was touting the passage of the farm bill and pledging to do more on the executive front, the limits of his strategy were apparent. The president opened his remarks by addressing the Labor Department jobs report released Friday, which showed the private sector added 140,000 jobs last month — sluggish numbers that again disappointed economists.

The president’s smaller-bore executive actions are unlikely to make much headway in that regard. The White House said Obama had lunch with Mayor Mike Duggan (D) of Detroit, a city whose bankruptcy illustrates the challenges that remain for a president who took over during a deep recession five years ago.

After his speech, Obama sat at a small desk — adorned with the presidential seal and positioned in front of the farming machinery — and signed the bill. Stabenow and the other Democratic lawmakers stood behind him and smiled.

“Can everybody see?” Obama asked.

Actually, it was unlikely that the Republican caucus back in Washington had even bothered to watch.

Ed O’Keefe contributed to this report.