"I think we're starting to get to the point where psychology is taking over," said Brad McMillan, chief investment officer for Commonwealth Financial. "You're seeing retail flows move back to equities. You have expectations in the institutions where the market is going to move up toward the end of the year. … Once you get disconnect from the fundamentals, you can drift as high as you want."
The Dow was above 16,000 again Tuesday, as Home Depot's strong earnings propelled its stock and the industrial average higher.
On Monday, stocks pulled back from those big round numbers and closed mixed, with the S&P off 5 at 1,791, and the Dow up 14 at 15,975, its fourth straight closing high. The Nasdaq, moving in on 4,000 early in the day, fell 36 points to 3,949.
The stock market gave up some gains when investor Carl Icahn told a conference just around 3 p.m. that he is cautious on the market, stocks are too expensive based on earnings and there could be a big drop. Legendary investor Jeremy Grantham's GMO joined the chorus, saying the S&P is well above its fair value of 1100, in a new report.
The Dow's run to 16,000 has been swift. It has risen nearly 1,300 points from its Oct. 9 low of 14,719. The S&P was at 1,646 that day.
(Read more: Icahn warns of market drop, shares give up gains)
"Right now greed has the lead." McMillan said. "There's a lot of people out there saying this is a bubble, and as long as people are saying that—it's not a bubble. This conceivably could go on for a while. Market trends could continue longer than you think, but at some point trends reverse."
The big round numbers are not meaningful for the market per se, but they are important to investor psychology.
"It's certainly going to bring light to the fact the market is as strong as it is," said Jack Ablin, CIO of BMO Private Bank. "Once we start crossing milestones it does kind of envelope a larger group of people, and there's going to be some people that look at it and say this means it's time to get in."
Ablin is a bit more cautious with the S&P's average price-to-earnings ratio over 17. The P/E represents the price of a stock divided by its earnings per share, and that average is usually under 16.
"I'm worried about a bubble," he said. "The metrics we track suggest the market is anywhere between 10 and 15 percent overdone if you pull the Fed out of the equation."
The market has been flashing plenty of warning signs, and its selloff in the final hour Monday was not a surprise after the series of record-setting sessions last week. For instance, the defensive telecom sector was the best performer Monday, and commodities-driven materials and energy were among the biggest losers. Both sectors rely on global growth.
(Read more: After getting crushed, this sector could be golden)
"We're in this hot potato market right now, where momentum is driving it," said Peter Boockvar, chief market strategist at Lindsey Group.
The small cap Russell 2000, off 0.8 percent, and Nasdaq, were again diverging on the downside, a negative sign to some traders who look for growth and small cap sectors to lead the market. Both are up more than 30 percent this year, while the Dow is up 22 percent and the S&P 500 is up 26 percent.
"We're due for a rest here," Boockvar said. "There's no question about it, but the bull market doesn't end until interest rates move back to 3 percent. I'm getting more bearish here. Many things are lining up. I think this is the last phase of the bull market."
But analysts agree that it's unlikely the stock market would see a pullback of more than several percent until next year—possibly around the time that Congress refocuses on the budget and debt ceiling, or if the Fed signals it will begin to reduce its $85 billion-a-month bond-buying program.
"The market hasn't cared about a mediocre economy. it hasn't cared about slowing earnings. It hasn't cared about Syria. The only thing I look for to reverse it is when the Fed becomes a factor, or the bond market does it for them," Boockvar said.
Another red flag for stocks is that investors have also been taking on record amounts of margin debt. According to NYSE Euronext, margin levels, or the amount borrowed to purchase securities, climbed to a record $401 billion in September.
(Read more: Larry Summers and the never-ending bubble economy)
Barry Glassman, president and CIO of Glassman Wealth Services, says the individual investors he speaks with are concerned about the market's run.
"The biggest challenge that I'm hearing from clients, as well as prospective clients, is they don't know what to do with their cash," he said, adding that they see bonds and stocks as pricey. "They don't want to be the people who plow money into the market at all-time highs.
"They are going through what we call financial schizophrenia," Glassman said. "They're going to go through those kinds of challenges, and they're left sitting on the cash. No decision is their decision."
One strategy he's recommending is to put some cash into long/short equity funds.
"These are strategies that are going long stable, or value companies, and shorting the high fliers," Glassman said.
There are plenty in the camp who believe the market can go higher until the Fed removes some of its stimulus, but there are also investors and money managers who expect to continue chasing performance into the year-end, fearful of losing out on potential gains.
—By CNBC's Patti Domm. Follow here on Twitter @pattidomm.