The NYT is a great newspaper with many outstanding reporters, but does it have access to the innermost thoughts of top administration officials? That seems unlikely, which is why readers should be wondering how it knows that "the administration fears it [a foreclosure moratorium] will only delay the inevitable and necessary process of forcing many Americans out of homes they cannot afford."
This particular explanation seems highly unlikely since its HAMP program seems designed to accomplish exactly this. The vast majority of homeowners who enter the HAMP program keep making payments on homes that they will eventually lose. While this does help the banks, it delays the inevitable and necessary process of forcing many Americans out of homes they cannot afford. It doesn't make sense that the administration would be spending tens of billions of dollars on a program whose main impact is to delay having homeowners forced out of their homes if it actually thinks it is important that people be forced out of their homes quickly.
There are other possible explanations for the Obama administrations opposition to a foreclosure moratorium. For example, it could be discovered that the fraud and procedural abuses are widespread. It would likely be very costly for many servicers to construct the proper paperwork to carry through foreclosures. The administration may not want to force banks to incur these costs. That is at least one alternative explanation for the administration's position.