Political pressure mounted on President Obama as the nation’s jobless rate shot up to 10.2 percent, a 26-year high that prompted blistering Republican attacks on his economic policies.

Republicans launched assaults against the president’s $797 billion economic stimulus package within minutes after the announcement yesterday morning that the jobs situation got much worse last month.

“Since President Obama’s inauguration, the nation has watched the unemployment rate continue to climb, and unfortunately the month of October was no different,” said Michael Steele, chairman of the Republican National Party Committee.

“With so many families looking for work, it is time the Obama administration stop spreading their phony ‘saved or created’ talking points and start creating the dependable jobs America needs.”

But the president stepped out into the White House Rose Garden yesterday to pronounce he was signing a new multibillion-dollar stimulus bill that includes extension of unemployment insurance benefits for the jobless and expansion of the homebuyer tax credit. He said his economic team is evaluating other options to create jobs and get the economy moving.

“I promise I won’t rest until America is prosperous once again,” Obama vowed.

Barry Bluestone, dean of Northeastern University’s School of Public Policy and Urban Affairs, said he expects the national unemployment rate to rise into 2010.

“Firms will not hire until they are certain that the economy is recovering,” he said. “Once firms are convinced that things are picking up, you’ll see a flurry of hiring.”

Ryan Sutton, vice president at Robert Half International, said his staffing firm is noticing very early signs of recoverey that could ultimately produce jobs. There’s been a small uptick in requests for temporary hirings in the Boston area, suggesting employers are gaining confidence about the economy, he said.

“We’re definitely seeing some positive signs,” he said.

Financial services, health care and the IT sectors are all seeing an uptick in temporary hires, he said.

The Massachusetts jobless rate was 9.3 percent in September. October numbers won’t be available until later this month.