However, Fed watchers are divided and say the Fed needs more evidence in November's jobs report that the employment gains are sustainable, and some say it will need several more months of proof. The economy added 204,000 jobs in October, well above the 125,000 expected by economists, and a shocker to a market that expected to see a big miss rather than a gain due to the government shutdown. Another 60,000 jobs were added to August and September in revisions.
Traders immediately dumped bonds, stock futures turned lower and then the market rallied later. The 10-year yield jumped to 2.75 percent, from 2.60 percent earlier in the morning. The dollar index also moved higher, up 0.6 percent to 81.35.
"The three-month average on payrolls is back at 202,000. It's all here. GDP is printing 3 percent. We have to stop thinking the shutdown had some impact.," said Joseph LaVorgna, Deutsche Bank chief U.S. economist. "Good news is now bad news (for markets). The Fed might taper sooner."
Moody's Analytic chief economist Mark Zandi said the number looked too good to be true, and he thinks the Fed has too little information to pare back its quantitative easing program. He said it will be several months before it can get a clear reading on employment.
"I'm surprised. I think it's bizarre. My sense is this is going to get revised down, or we'll get some weaker number going forward. I just can't see the government shut down and brinkmanship not doing some damage to the job market," he said.
"The percent of companies that responded to the survey was inordinately high. It was around 83.5 percent. It was typically more like 60 percent. It may be that they had more time to respond." Last month, the percent of companies responding was 72 percent. This month, the government delayed releasing the jobs report by a full week.
JPMorgan economists, on the other hand, said the strong report makes it more likely the Fed will slow its bond buying sooner than the March time frame it had expected.
"This stronger trend shifts the expected timing of the Fed taper of asset purchases to January (from March-April). The timing could be earlier if the labor market continues to surprise on the upside and could be later if the fiscal negotiations are drawn out," they wrote.
(Watch: What will jobs do to bonds?)
The October report, however, did contain plenty of negatives. The unemployment rate climbed to 7.3 percent and households reported a huge decline in employment. The measure that shows the underemployed and those who stopped looking also rose, to 13.8 percent from 13.6 percent.
"Certainly this report is clouded. Good news on the payroll front though half the gains are in leisure, hospitality and retail, which means they were hiring for the season," said Mesirow Financial's chief economist, Diane Swonk. "The fall in employed workers was larger than expected. ... We've got these two conflicting reports."
(Read more: So much for that 'disposable' October jobs report)
Swonk said even though the report is inconclusive, the Fed will have a heated debate about "tapering" its $85 billion bond-buying program at the December meeting. Many economists have expected the Fed to wait until March because of the uncertainty about the government shutdown on the economy and hiring.
"It provides more questions than answers but it fuels the debate about how do we begin tapering," she said. "They really are uncomfortable with the balance sheet. They really do want to extend the forward guidance until 2016 and leave that punch bowl out there longer."
The Fed has now guided markets to expect it to keep its target funds rate near zero until 2015, and has used the bond purchases to pressure longer-term rates and push investment to riskier assets.
But Swonk expects the Fed to shift its focus to emphasizing low rates for longer while paring back on the bond purchases.
(Read more: Why small caps may signal bigger problems: Pro)
"Bottom line, even with my skepticism I think it goes to the underlying strength of the economy," Zandi said of the jobs report. "We've got all these ups and downs every month and yet we still produce 175,000 jobs every month, no matter what we throw at the economy."
—By CNBC's Patti Domm. Follow here on Twitter