House Speaker John Boehner, R-Ohio, then confronted Obama on the president's claim Republicans had yet to put forward a plan that would create jobs right away.
"The last time I was here at a press conference, I asked you guys to show us the Republican jobs plan that independent economists would indicate would actually put people back to work. I haven't yet seen it," Obama told reporters during a press conference earlier Thursday with South Korean president Lee Myung-bak.
"And so, eventually, I'm hoping that they actually put forward some proposals that indicate that they feel that sense of urgency about needing to put people back to work right now," Obama said.
Boehner "respectfully challenged" Obama on this during a 10-minute phone call Obama made to Boehner to congratulate him on passage of three free-trade agreements Wednesday, Boehner's office said.
"I want to make sure you have all the facts," Boehner told Obama, the speaker's office said.
Boehner then pointed to measures House Republicans introduced in May, dubbed the "Plan for America's Job Creators," which included the trade pacts and proposals to roll back federal regulations and cut business taxes.
He said he and other GOP leaders had spoken with Obama and his staff about the plan on numerous occasions.
He said the House Ways and Means Committee Thursday approved a bill to block permanently a planned 3 percent withholding tax on government contractors. The bill is expected to clear the House in the next two weeks.
"The speaker expressed his desire to do something on the issue, but to do it in a fiscally responsible way," Boehner's office said.
White House spokesman Josh Earnest declined to discuss details of the call, but said Obama was "very clear that he is willing to work with Democrats and Republicans to pass measures to create jobs and get our economy moving."
He said independent economists have called Obama's American Jobs Act "the only plan that will create jobs and help the economy now."
Thursday's GOP plan -- written by Sens. John McCain of Arizona, Rob Portman of Ohio and Rand Paul of Kentucky -- would repeal the 2009 healthcare-reform law and the Dodd-Frank Wall Street Reform and Consumer Protection Act that imposed sweeping financial-regulation changes after the 2008 economic meltdown.
In addition, it would lower tax rates, eliminate corporate loopholes and impose a temporary moratorium on new government regulations until the U.S. unemployment rate drops to 7.7 percent, its level when Obama took office in January 2009. The rate is currently 9.1 percent.
"We just thought it was time to put this all into a package" that could compete with Obama's $447 billion jobs bill, which the Senate rejected this week," McCain said at a news conference Thursday to unveil the legislation.
"I will freely admit to you that part of it is in response to the president saying we don't have a proposal," he said.
Bill supporter Sen. Lindsey Graham, R-S.C., added, "We have to be for something."
Paul said the bill would create 5 million jobs, but didn't offer a time frame.
The lawmakers said their package could inject certainty into the economy by limiting government involvement they say stifles growth. They call Obama's plan a temporary quick fix requiring government spending that will do nothing to improve the economy in the long run.
Sen. Charles Schumer, D-N.Y., criticized the GOP proposal as "a political fig leaf that would likely add to the deficit while doing nothing to create jobs."
Sen. Carl Levin, D-Mich., said, "It doesn't sound like a jobs bill -- it sounds like a Republican theology ... like a rehash."