The Peoples' Party is using its absolute majority to keep Rajoy from chiming in on the Bárcenas case in Congress and the supposed bonus payments that party leaders received, including the Prime Minister himself. This is not a good strategy for the government to employ.
Rajoy is not expected to issue any rigid proclamations (that's what the courts are for), but simply to fulfil his political obligations by participating in the governmental process. That means talking with Congress. The Spanish people don't understand why Rajoy is staying quiet, and they interpret his silence as an indicator of guilt.
Hiding behind the shield of an absolute majority raises suspicions, hurts our global reputation and has serious political and economic fallout for a country trying its hardest to end a crisis and face major sacrifices.