President Obama's failure to stand his ground in ongoing negotiations with Republicans on key issues from taxes to jobless benefits has stirred howls of protest from many of his supporters on the left who are beginning to question the president's leadership skills.

Supporters say Obama should have been able to close the deal by now on extending the Bush tax cuts for only middle- and lower-income households and renewing another round of unemployment insurance.

Instead, Obama continues to extend his hand to Republican leaders who have made clear that any compromises with the White House on spending and tax cuts would have to be on their terms.

One liberal group, the Progressive Change Committee, is circulating a petition telling Obama that "Americans want him to fight the Bush tax cuts for millionaires – and that Democrats will keep losing if he keeps caving."

Yet there are some veteran Democratic analysts who say it's not time to hit the panic button yet.

"Forgive me if I sound a bit jaded. I've heard it before," said Bill Galston, a former top aide to President Bill Clinton who served in the administration when Republicans captured Congress two years after Clinton took office. Galston told FoxNews.com that there was a six-month period when "Clinton couldn't do anything right" and he was seen as increasingly "irrelevant."

"And somehow he was re-elected handsomely in '96," he said.

But Obama continues to suffer setbacks one month after Republicans crushed Democrats in the midterm elections, capturing control of the House in a landslide and increasing their ranks in the Senate.

On Saturday, Senate Republicans rejected two proposals extending the Bush tax cuts for all but the wealthiest households, prompting Obama to say he was "very disappointed" but determined to find a solution in further negotiations. Obama has said he is willing to back a temporary extension of tax cuts for households earning over $250,000 per year.

Obama further enraged his supporters when he announced this week he wanted Congress to freeze the pay of civilian federal government employees as a step toward cutting the huge U.S. budget deficit. The unions have vowed to fight the proposal and Democrats have called it short-sighted.

Liberal economist Paul Krugman wrote in his New York Times column this week that Democrats will have to look elsewhere for leadership.

"It's hard to escape the impression that Republicans have taken Mr. Obama's measure – that they're calling his bluff in the belief that he can be counted on to fold," he wrote. "And it's also hard to escape the impression that they're right."

But Galston said Obama's leadership may not be a problem at all.

"I guess the question is whether we're talking about issues of style or issues of fundamental objectives," he said. "We may also be talking about questions of what's feasible in given circumstances."

"And it may very well be with regard to the latter, that the president has reached a judgment that will not be fully accepted by the members of his own party, particularly in the House of Representatives," he said. "They may continue to believe certain things are possible that the president doesn't believe is achievable."

But Matt Schlapp, a former White House director in the second Bush administration, said Obama may have problems that go beyond differences between him and his party.

"I think most Republicans are looking at the White House and saying who's running shop? How are they making these decisions," he told FoxNews.com.

"And when you have 9.8 percent unemployment and the economic situation the country is in, there seems to be a glaring lack of presidential strategy to encourage Americans that better economic times are coming," he said.

Schlapp said he was most confused by Obama to signal he's willing to extend the Bush tax cuts on all households temporarily and then continue to stake out a position for letting them expire on the upper income brackets.

"Every appearance from the outside looking in suggests he doesn't seem to be aware of how serious his problem is in terms of the tone of his policies or he's just a left-wing college professor from a big city who is disdainful of what these Americans want," Schlapp said. Or he believes he can bamboozle them into thinking these policies are what they want."