Separated by 16 miles, but a world apart philosophically, President Obama and a chief Republican adversary staged separate events here Friday, launching another round in their public battle over jobs and the economy.

Obama arrived first at the University of Richmond shortly before noon, appearing more than three hours before House Majority Leader Eric Cantor would return to his home district to offer some strategic counter-programming.

In front of 8,000 enthusiastic college students in a campaign-style rally, Obama made an impassioned plea for help to convince Congress that “the time for action is now” on the $474 billion jobs bill he had unveiled the day before.

The president hammered away on a refrain that he used in a Thursday speech to Congress — “pass this bill now” — as he made the case that his administration is addressing the jobs crisis with urgency even as the rest of Washington dithers.

“The next election is 14 months away. We cannot wait,” Obama, tieless, with his sleeves rolled up, told the audience, who interrupted him with shouts of “We love you!”

“The American people do not have the luxury of waiting the next 14 months for action,” Obama continued. “Some live paycheck-to-paycheck, week-to-week, day-to-day. Now is not the time for people in Washington to worry about their jobs; it’s time for them to worry about your jobs. It’s time to put America back to work. It’s time to act.”

Cantor, the House’s most hard-line negotiator with Obama during the debt ceiling debate, turned down an invitation from the White House to attend the rally. He remained in Washington for a vote on an intelligence reauthorization bill.

Cantor’s event at the Titan America concrete facility had a starkly different feel from Obama’s. He was greeted by three dozen company employees sitting on white folding chairs under a tent on the pavement of the parking lot, two dump trucks parked behind him.

Titan, its local president explained, had suffered during the economic downturn, falling from 900 employees in Virginia in 2007 to 500 this year. And the company was worried about more burdensome government regulations set to take effect soon.

The House leader, who like Obama wore no jacket or tie with his white dress shirt, laid out a competing philosophy in which less Washington red tape would allow businesses to invest in new jobs.

“He believes in a fair shake but also believes somehow we ought to raise taxes on some he feels are not paying enough,” Cantor said. “We feel we should unleash the entrepreneurial nature of people . . . so that we have earned success instead of success for some by guaranteed outcomes directed by the government.”

The White House viewed Obama’s speech before Congress Thursday and the appearance in Richmond as the start of a campaign to force congressional Republicans to the bargaining table or risk being painted as doing nothing to help struggling Americans, according to Democratic sources familiar with the administration’s strategy.

Obama’s choice to open his tour in Cantor’s district was a direct challenge to the Republican who has perhaps caused him more grief than any other over the past several months. During a tense moment in the debt negotiations, Obama reportedly told Cantor: “Don’t call my bluff, Eric. I’m going to the American people with this.”

Republicans have since gained the upper hand, with much of Obama’s liberal base frustrated that the president has not negotiated strongly enough.

Obama told the crowd here that he was glad to hear some Republicans express willingness to consider some of his jobs proposals. When some students responded with catcalls, Obama said: “I know sometimes folks think they’ve used up all their benefit of the doubt, but I’m an eternal optimist.”

The students cheered.

“But we’ve got to give them a little help to do the right thing,” Obama continued. “So I ask all of you to lift up your voices, not just here in Richmond, but anyone watching, following online: call, e-mail, send a letter, tweet, facebook, send a carrier pigeon. Tell your congressperson the time for gridlock is over. The time for action is now. Pass this bill!”

Across town, Cantor told his audience that he and his fellow Republicans were aiming to seek common ground by finding some parts of Obama’s jobs plan that they can support. He pointed to tax breaks for small businesses and easing regulations on companies making investments in new projects.

With Congress’s own approval ratings even worse than Obama’s 40 percent, House Republicans have launched an effort to appear more conciliatory, just as Obama tries to get tougher. But Cantor was not willing to let Obama’s comments at the rally pass without a stern rebuke.

“I object to the all-or-nothing message the president is delivering. That’s not how anybody operates,” he said. “My response to the president is, is he going to work with us? If we put forward a bill that peels off some of his package and some of the ideas we talked about today, is he going to work together with us?”