Grohowski said the poor jobs report, the weakest since December 2013, signals the Fed is likely to take its time raising rates. After the Fed's March meeting, markets read the Fed statement and forecasts to mean a rate hike in September was more likely than June. The poor jobs number reinforced the time frame as September, or even later.
Read MoreJobs report signals Fed on hold until second half
Goldman Sachs economists said in a note that while they expect the first hike in September, the weak jobs report raises the risk of a later liftoff in rates.
The jobs report also makes the minutes from that last Fed meeting, released Wednesday, an even more important event in the coming week, as well as the comments from Fed speakers. New York Fed President William Dudley is the first Fed speaker of the week when he discusses the economy in Newark, New Jersey, Monday morning. His comments will be given added weight as he is viewed as closely aligned with Fed Chair Janet Yellen.
Diane Swonk, chief economist at Mesirow Financial, said the Fed minutes may reveal more about how the Fed came to its decision to raise rates but also more about why it expects to go slowly. The jobs report "affirms Yellen's dovishness relative to her cohorts. They want to get liftoff this year, but oh so gradually. They'll be treading as if on thin ice," she said.
"As we look at the minutes, it will affirm the doves' view that we need more improvement in the labor market," Swonk said. At that meeting, the Fed removed the word "patient" from its statement, signaling it was nearing a decision to raise rates but also that it would now rely heavily on economic data in its decision making.
Read MoreJobs creation big letdown in March
Swonk said it will be key to see what the Fed said about employment. "There are a lot of nuances to removing patience that didn't really remove patience. They went from patience to caution," she said.
The March employment report was the latest data to confirm sluggish first quarter growth, showing up in manufacturing and other data. Economists' expectations for first quarter growth is now tracking at 1.3 percent, according to CNBC/Moody's Analytics snap survey.
Even as economists expect a very weak first quarter, they also expect to see a rebound in the second quarter with growth pegged at more than 3 percent. It will be key to see if Fed officials see a change in the outlook, as that would affect expectations for the timing of a rate hike.
"We will see a spring back. We know some things are transitory. That's the good news. Even as it's transitory, new head winds are emerging. That's the strong dollar and lower oil prices," Swonk said.
Besides the Fed minutes, there is also a first trickle of quarterly earnings reports, starting Wednesday with Alcoa. Markets will also be watching the drama around Greece's pending payment to the IMF.
"I presume (the Fed) was inching closer to doing something because they thought the numbers were particularly strong. Now, you've got a 69,000 revision (in January and February) and you've got a weak March number, so net, net things look 250,000 weaker," said Amherst Pierpont global strategist Robert Sinche. He said the Fed's path is now less clear. "The jury is very much out. You just don't know how much of this is temporary factors."
Grohowski said he still expects the Fed to boost the fed funds rate by 50 basis points by the end of the year, but liftoff will now be September at the earliest.
"We're still in a market that, at some point, is going to have to deal with higher interest rates. Meanwhile, the earnings side is going to come into greater focus here," he said. Both of those factors could create a more volatile environment for stocks this year.
Grohowski has favored big cap U.S. stocks since the bull market began six years ago but this is the first quarter where he is concerned that there's a potential for stocks to become overvalued this year because of lower earnings growth and rising interest rates.
S&P 500 earnings for the first quarter are expected to decline nearly 3 percent, the first negative quarter in six years. The strengthening dollar and falling oil prices are two key factors biting into corporate profits and the economy.
"We are no doubt in a mini-earnings recession," Grohowski said. He has not shifted his allocation of U.S. large cap stocks yet but would consider doing so when the S&P 500 reaches his 2,200 target.
"I think that the first quarter of the year gave us a very good window into what this year could be like as a whole and certainly what the next quarter will potentially be like," he said.
Read MoreFirst quarter ends but market volatility will not
In view of the potential for higher rates, Grohowski said price-to-earnings ratios have become stretched. Based on his earnings forecast, the S&P is looking at a P/E of 18 times.
The few economic reports in the week ahead include ISM nonmanufacturing data, JOLTs job openings data, weekly claims and wholesale trade. There are also auctions of 3- and 10-year notes as well as the 30-year bond.