1. If people (such as creditors or customers) know that the government or the Federal Reserve is going to bail out any failing large bank (especially, politically-favored ones), they will lend to it with less concern about the risk than would otherwise be the case. In 2008, the government forced the nine largest banks to accept TARP money whether they wanted it or not, and also bailed out others.
2. If big bankers know that government will step in and help them if they make bad decisions that result in big losses, they will be less careful than otherwise in operating their banks. Also, their response to competition will be skewed, because they know other big banks enjoy that same assurance. Thus we have essentially a cartel of large banks, protected by the Fed (whose main purpose is to protect large banks) and the government.
3. When the government creates a multi-billion-dollar special fund, the expense ultimately belongs to the taxpayers.
4. A government program to protect any “too big to fail” bank or private business of any kind is a violation of public trust, and an unjust burden on taxpayers.
In Treasury Secretary Timothy “Bailout” Geithner’s Washington Post op-ed, he says,
Crucially, if a major firm does mismanage itself into failure, the Senate bill gives the government the authority to wind down the firm with no exposure to the taxpayer. No more bailouts. Instead, we will have a bankruptcy-like regime where equityholders will be wiped out and the assets will be sold.
These are important steps, but they are not enough. Ending "too big to fail" also requires building stronger shock absorbers throughout the system so it can better withstand the next financial storm. To do that, the Senate bill closes loopholes and opportunities for arbitrage, and it brings key markets, such as those for derivatives, out of the shadows… 
No more bailouts? Read on.
Geithner also says,
All of that [new regulation] means major global financial institutions -- whether they look like Goldman Sachs, Citigroup or AIG -- will be required to operate with less leverage and less risk-taking.No exposure to taxpayers? As Conn Carroll at The Heritage Foundation reports,
But does the Senate bill’s “bankruptcy-like regime” solve the “too big to fail” problem? No. In fact it makes it worse. What the Dodd bill actually does is create a new $50 billion fund to be used in “emergencies” for restructuring firms deemed too close to bankruptcy. And who gets to decide when there is an emergency and which firms are too close to bankruptcy? You guessed it: Treasury Secretary Timothy Geithner. The Dodd bill is thus nothing but a permanent extension of Secretary Geithner’s TARP powers.  (Emphasis added)
So, put briefly, the government wants to take unto itself micro-management of financial institutions, telling them what kinds of business and risks they can and cannot deal with, and also the government would acquire the ability to take over any financial institution they please, whenever they please, and force it to quit business and be split up.
If the Administration is actually concerned about “too big to fail,” they would simply say OK, no more bailouts, period. If bankers know they will never be bailed out, they will choose to operate with less risk, and will be more careful in their decisions. If you go under, you go under, and normal procedures (bankruptcy, etc., not a “bankruptcy-like regime”) will be followed. If it messes up the system, so be it, the market is self correcting. With the government’s “bankruptcy-like regime,” the Administration, not a bankruptcy court, will rule, and Geithner (read: Obama) gets to pick board members, etc. Also, he will pick winners and losers since he would have complete authority to decide what institutions need to be dealt with under this bill.
The government seeks to impose new regulations, and some regulations are needed. The needed items could be added simply by updating some SEC rules (such as overseeing derivatives). But this is the wrong approach, and, in effect, just makes TARP permanent and arbitrary enforcement inevitable. What this government “regulates,” beyond existing rules, they will seek to take over. When Congress gives them a blank check, they will use it to redistribute wealth and take more control. Geithner also discusses an “international” system of similar controls which the Administration would like to see. Our entanglement in other countries’ financial troubles is already beyond reasonable limits. We don’t need any more.
As usual, in President Obama’s proposed laws, the “Secretary” gets vast power. Thus Obama gets vast power. His already fascist regime is constantly working on new takeovers and ways to remove individual freedom and decimate the private sector. Even if the Supreme Court eventually rules some of his initiatives unconstitutional, it may be too late to stop the destruction they cause. That happened under the New Deal.
An AP article by Jim Kuhnhenn reports,
Aides said Senate Republican Leader Mitch McConnell in the meeting urged Obama not to cut off bipartisan talks. Afterward, McConnell still insisted that the Senate bill “will lead to endless taxpayer bailouts of Wall Street banks.”
That was the message McConnell delivered earlier Wednesday on the Senate floor — the second such attack on the bill in as many days. He said the White House plans the same approach on financial reforms that it took on health care: “Put together a partisan bill, then jam it through on a strictly partisan basis.”
White House economist Austan Goolsbee dismissed the GOP objections as “totally disingenuous.”
“Bailouts are forbidden,” he said in an interview. “There will only be wipeouts. They (the banks) will clean up the messes. If somebody fails, they're done — they're toast. The management is fired. They're broken up or sold off or liquidated.” 
But McConnell is correct. One may hope the Republicans can filibuster this.
 Timothy Geithner, “How to prevent America’s next financial crisis,” 04/13/2010, Washington Post.
 Conn Carroll, “Wall Street Bailouts Forever,” 04/14/2010, The Foundry blog, Morning Bell, The Heritage Foundation.
 Jim Kuhnhenn, “Obama, GOP wrangle over Wall Street regulations,” 04/14/2010, Associated Press via Google News.