"Tell them to stop worrying about their jobs and start worrying about yours because we're all in this together, and together is the way we're going to bring America back even stronger than it was before," Biden said.
Obama, who returned to Washington late Friday after attending an economic summit in France, made a similar appeal in last week's address.
Biden said as opposition from Republicans continues, the president has used his executive authority to help veterans find jobs, homeowners refinance mortgages, and reduce the cost of student loans.
Biden said those efforts would continue so long as Republicans oppose the president's plans.
"If the Republican Congress won't join us, we're going to continue to act on our own to make the changes that we can to bring relief to middle-class families and those aspiring to get in the middle class," Biden said.
Last month, Republicans blocked the $447 billion package and then Democratic efforts to win approval of a $35 billion piece of the legislation intended to prevent layoffs of teachers and firefighters.
Obama presented his jobs plan in September and has since launched a campaign-style effort to win passage, holding rallies in states critical to his re-election efforts.
In the GOP's weekly address, Massachusetts Sen. Scott Brown urged Senate passage of legislation that would repeal a 3 percent withholding mandate on payments to many contractors who do business with the federal government.
Brown called it "a stealth tax" that will hit small businesses and contractors starting in 2013.
"Now, all the mandate will do is, is take more money out of our economy at a time when quite frankly we can least afford it. And as a result, businesses will have less money to hire and pay new workers," Brown said.
The repeal passed the House last week with wide bipartisan support and Brown called on the Senate majority leader, Democrat Harry Reid of Nevada, to bring it to a vote.