As billionaire investor Carl Icahn snaps up shares in Time Warner in a bid to push the media giant to pursue a plan he thinks will boost the stock price, the growing sense on Wall Street is that he is not likely to get much of what he wants.

Thanks to the sheer size of Time Warner’s investor base, the success that Time Warner’s management has had at running its various businesses, and a general belief among investors that there’s not much wrong with the company, save its stock price, Mr. Icahn will probably face an uphill battle using his modus operandi as a corporate raider to effect change at the company, several analysts said last week.

“Due to the size of the company, the investor group [led by Mr. Icahn] is unlikely to be able to accomplish much on its own,” Merrill Lynch analyst Jessica Reif Cohen said in a research note. “We therefore believe that the ultimate success in its place being executed is dependent on gaining significant support from other institutional investors. … However, the road could be more difficult than Mr. Icahn has encountered in other investments, as even frustrated investors admit management has a relatively strong track record.”

Mr. Icahn met last Wednesday with Time Warner Chairman and CEO Richard Parsons for what he described as a “good and productive” sit-down. Mr. Icahn shared with Mr. Parsons his ideas for helping to lift Time Warner’s shares, which have languished under $20 a share for the past three years.

“At the end of the meeting, we both observed that we had, at the very least, one thing in common: We both believed Time Warner was meaningfully undervalued and that we both wanted very much to rectify this situation,” Mr. Icahn said in a statement released last Thursday.

The meeting came after Mr. Icahn’s hedge funds, Icahn Partners and Icahn Partners Master Fund, along with Franklin Mutual Advisors, JANA Partners and SAC Capital Advisors, confirmed last week that they are acquiring Time Warner shares as part of a broader move to push the media company to increase the size of its share buyback program to $20 billion from a current level of $5 billion, and to completely spin off its cable unit, versus the company’s current plan to offer 15 percent of Time Warner Cable to the public.

Perhaps the biggest challenge facing Mr. Icahn and his quest for change at Time Warner will be amassing enough shares to carry any influence on Time Warner’s board of directors. Indeed, according to a statement released by Mr. Icahn early last week, two hedge funds he owns, along with three other Time Warner investors that have agreed to back Mr. Icahn’s Time Warner moves, collectively owned 120 million shares worth around $2.2 billion-less than 3 percent of the total shares outstanding. Time Warner’s market capitalization is nearly $86 billion.

“This company has a huge market cap, which makes this an awfully big project to undertake,” said Harold Vogel, CEO of Vogel Capital Management and a longtime media analyst. “It’s a mistake [to pursue this].”

To be sure, Mr. Icahn has an impressive track record as both a corporate raider and an activist shareholder. In the 1980s he waged takeover battles for companies such as Texaco, the former Trans World Airlines and rail company USX. In the 1990s he did it again, forcing RJR Nabisco to sell off its food and tobacco businesses, which the company did in 2000 to Philip Morris, helping Mr. Icahn earn a profit of $900 million.

More recently Mr. Icahn set his sights on struggling video retailer Blockbuster, staging a coup that gave him control and led to a board shakeup at the company.

But some analysts are suggesting that in turning his attention to Time Warner, he might have trouble working the same sort of magic that over the years has allowed him to be so successful. Forbes magazine says he’s worth nearly $8 billion.

Mr. Vogel noted that Time Warner is one of the most widely held stocks around and is closely watched by many analysts. In other words, it is a very different company from those Mr. Icahn has gone after in the past.

What’s more, Mr. Vogel and other analysts say Time Warner is unlikely to completely shed Time Warner Cable due to a huge tax bill that could result for the company.

Then there’s the issue of timing. Merrill Lynch’s Ms. Reif Cohen pointed out that the Icahn group is gearing up at a time when most investors believe the company is going in the right direction.

“There could also be a significant number of investors who do not welcome this sort of distraction at a time when the company already has plenty on its plate,” she said, referring to its ongoing acquisition of bankrupt cable company Adelphia Communications and efforts that are under way to improve its online unit, America Online.