Even though the Fed is pressing, many Fed watchers still say the Fed may wait to hike, not wanting to get in the way of the November presidential election. But Tannuzzo disagrees. "I don't buy the election impact. They have done a lot of very aggressive policy in election years and at meetings around elections," he said. However, he noted that more of the pre-election policy moves have been easing, not tightening.
"I think it would be foolish to ignore that a strong jobs number next Friday is something that could actually make the Fed move. I think the market will take it seriously if we have a strong number," Tannuzzo said. "If we have a lousy number, sure, you would take the Fed off the table."
Goldman Sachs economists Friday said their expectations for a September hike rose to 40 percent, up from 30 percent after the Jackson Hole comments. Their odds for a hike this year rose from 75 percent to 80 percent.
"Although neither Yellen's comments nor those of other officials have been explicit on the precise timing, this may reflect message discipline ahead of the August employment report to be released next week," the Goldman economists wrote. "In our view, if the employment report continues to indicate an improving labor market, the FOMC may well raise rates at the September meeting."
Some market participants say, however, anticipation about a rate hike could create enough volatility to trigger a tightening of financial conditions that would keep the Fed on hold for September.
But Grohowski sees stocks continuing to grind higher, and he says it's still more likely the Fed hikes rates in December.
"Economic data on balance has been improving, and then I think through all of this, there's still this optimism that central banks are going to remain supportive and supportive of what it takes to keep the economy afloat. I think that argues for a market that grinds higher," he said. The Fed is moving alone to tighten policy, as other central banks are easing. That has kept interest rates low in the U.S. and helped lift risk assets, but it also makes it more precarious for the Fed if the dollar shoots higher.
Grohowski said the stock market has exceeded his year-end target of 2,150 on the S&P 500, and he is looking at 2,300 or 2,350 for the end of next year.
For now, the U.S. presidential election is not a concern for markets, though comments from Democrat Hillary Clinton about Mylan's pricing of EpiPen hit that stock hard and sent the S&P health-care sector lower. The sector was down 1.8 percent for the week, second only to utilities, down 2.3 percent for the week. Utilities decline with rising rate expectations since they are popular for their dividend yields.
"I think the market has become accepting of a Clinton victory," he said. "I do think there's some time to go here, so if there's a change in that, that too would increase market volatility. If it looks like the election starts to look like it's a close one, that would be potentially disruptive to the market."
Stocks were mixed Friday on the highest volume in three weeks. The S&P 500 fell 3 to 2,160, while the Nasdaq was up 6 at 5,218. For the week, the S&P 500 lost 0.7 percent. The Dow was down 0.8 percent at 18,395 and the Nasdaq was down 0.4 percent at 5,218.
The dollar index, at 95.46 late Friday, was up 1 percent for the week. Oil was volatile, declining about 3 percent, after the week earlier's 9 percent gain.
As for Treasurys, the two-year was at about 0.84 percent Friday, a level last seen on June 3. The 10-year yield broke out to 1.63 percent, the highest level since June 24. It had been in a range between 1.50 and 1.59 percent for the entire month of August.