The Fed came into focus after the June jobs report, with speculation rising that it may need to move sooner to raise short-term rates if the economy keeps improving. That report showed a surprise gain of 288,000 nonfarm payrolls and the unemployment rate down to 6.1 percent.
Mark Zandi, chief economist at Moody's Analytics, said it's unlikely the Fed will come off the sidelines until this time next year, but that would change if job growth continues to build.
"If we continue to get these kind of job numbers, they're going to have to change the trajectory for interest rate hikes," he said.
Levkovich said the Fed could become a real focus for the stock market as it reaches the end of its quantitative easing program. As the Fed gradually winds down its bond buying, the market could start to see a change in tone, as investors look forward to the onset of the Fed's first rate hike.
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"We could be sitting here in the third quarter or fourth quarter, where everybody's focused on the Fed and the market could run into volatility," he said.
Anticipating the Fed's step back from easing has not been a good strategy, since stocks have continued to make gains, Levkovich added.
"I think in general, investors are still relatively cautious. They've missed the rally in most cases and are still struggling with that. What if the market melts up? It's a concern. I thought it would melt down earlier and it didn't," he said.
The Treasury holds auctions of the three- and 10-year notes and the 30-year bond on Tuesday through Thursday. Yields moved higher in the past week, both before and after the jobs report. The 10-year ranged from 2.51 percent early in the week to a high yield of 2.69 percent Thursday.
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"It's a big move, but it's not a game-changing event apparently," said David Ader, chief Treasury strategist at CRT Capital. "We're accommodating another piece of strong data. We'll look at it in the context of supply ... I think that the weakness we've had so far this week is more about the calendar than nonfarm payrolls."
Ader said he expects the 10-year yield could trade as high as 2.70/2.75 percent.
The Fed minutes on Wednesday could create some volatility for markets, as central bank officials may disclose some of their discussion on the return to normalcy, and analysts note they do not agree.
"We expect the FOMC minutes to be more hawkish than the public comments made by Chair Yellen, who has clearly been on the dovish side of the monetary policy spectrum, " wrote Deutsche Bank economists.