Reporting from Mesquite, Texas— Appearing on stage with a laid-off social studies teacher here this afternoon, President Obama suggested that opposing his full jobs bill is tantamount to opposing her gainful employment.

House Republicans should call a vote on his bill in its entirety, Obama said, so that Americans can see where every member of Congress stands on it.

But House Majority Leader Eric Cantor fired back from Washington that Obama's "my way or the highway approach" is impeding the search for common ground.

And Senate Republicans teased the president a bit by trying to take him up on the challenge, knowing that Democrat leaders are reluctant to call the measure right now. Sen. Mitch McConnell, the Republican leader, tried to force a vote on the president's proposal -- only to be shot down by Senate Majority Leader Harry Reid.

So the rhetoric intensified in the wake of Cantor's recent speculation that the American Jobs Act is dead, at least as the $447 billion package the White House is currently pushing.

Republicans leaders say they are willing to pass portions of that plan in the next month but not the proposal as a whole, with its proposed closures of tax loopholes and tax increases for the wealthy.

The GOP solution relies on spending cuts and tax breaks, which they contend would make companies more likely to expand and hire.

"If House Republicans sent our plan for America's job creators to the president, would he promise not to veto it in its entirety?" Cantor spokesman Brad Dayspring said Tuesday. "Would he travel district to district and explain why he'd block such common sense ideas to create jobs?"

In fact, Obama is responding to those ideas in his travels, at least in general terms. They're based on a "you're on your own, good luck" mindset, he told a group of supporters at a noontime lunch.

But his district-to-district travels are focused blatantly on the controversial parts of his plan, such as his proposal to spend $30 billion to help hire back laid-off teachers.

On Tuesday, in a speech at Eastfield College in Dallas County, the president put a spotlight on Kim Russell, a social studies teacher who lost her job teaching public school in May.

"I miss my students," Russell told the crowd, "and I miss my classroom."

The hire-back provision of his plan would put Russell back in that classroom, Obama said, but Cantor "won't even give it a vote."

"Mr. Cantor should come down to Dallas, look Kim Russell in the eye and tell her why she doesn't deserve to be back in the classroom doing what she loves," he said. "If you won't do that, at least put this jobs bill up for a vote so the entire country" can see who supports it and who doesn't.