One priority for the bureau will be to increase transparency in the marketplace. Consumers need to have full, clear information available to them in order to make well-informed financial decisions.
In a similar way, the Congress and the American people needs full transparency when it comes to individuals nominated for high-ranking posts. That's an essential component of the confirmation process. It serves, in part, as a fact-finding mission. The nominee's background, views, and experience are all discussed. Without a thorough investigation, a poor decision could be made and a flawed candidate could end up with a very important job.
To End "Unfair, Deceptive, or Abusive Practices"
A pretty clear cut goal of the CFPB will be to eliminate "unfair, deceptive, or abusive practices" (per its website). This is pretty straightforward when applied to lending.
But it applies to politics as well. To promote fairness, the president needs to give Congress a say on important nominees. To avoid deception, he should do so through an open process, rather than through a loophole that technically allows him to appoint someone to a post when Congress is in recess. Clearly, such an action would be an abuse of power, as his position doesn't allow him to push through such nominees under normal circumstances.
Adhering to the Law
You may have heard about the big foreclosure gate fiasco that began last fall. It turns out that some mortgage servicers were cutting corners and disregarding the proper procedures for processing foreclosures. The CFPB would certainly seek to ensure that this sort of behavior does not occur in the future. If financial firms fail to follow the rules and procedures in place, then consumers will suffer.
So how can the Obama administration possibly push a nominee for the CFPB through without confirmation? How would such an action be any less objectionable than banks processing foreclosures without following all of the required rules? The rule of law is sacred: shortcuts and loopholes that disregard its spirit should not be tolerated.
If this were a Republican president seeking to appoint a conservative director during recess that a Democratic Congress wanted to block, then the same rules would apply. This isn't a partisan issue, and it has nothing to do with Elizabeth Warren in particular. A recess appointment tactic would be be reprehensible, because such an action would go against the precise principles for which the CFPB stands.
*Update: A source informed me, on deep background, that this letter from Democrats is likely in response to a letter to the president from 44 Senate Republicans (.pdf) demanding "reforms" to the CFPB, which include putting a board of directors in place to oversee the bureau, subjecting it to the appropriations process, and establishing safety-and-soundness checks for the prudential regulators. Republicans in the letter say that if these changes are not adopted, they will block any nominee for the bureau's head.