From typicallyspanish.com

National
Esperanza Aguirre refuses to rule out running against Rajoy as leader of the Partido Popular
By h.b.
Apr 8, 2008 - 2:13 PM

The Partido Popular President of the Madrid Regional Government, Esperanza Aguirre, appears to obtaining support from certain sections of the party to challenge the leadership of Mariano Rajoy at the party’s conference to be held in Valencia in June.

On Monday she refused to rule out standing for the post, although told her audience at the ABC forum in Madrid, which included Mariano Rajoy, that it was not in her current plans.
Now the party’s spokesman in the Madrid assembly, Antonio Beteta has said that she is the best candidate to lead the party, and he claims that there are ‘numerous’ deputies which would support her.

However under the current party rules Mariano Rajoy is all-powerful as leader. He was personally chosen by the previous leader José María Aznar, and he has been in turn personally choosing his opposition team, preferring to select from those areas known to be loyal to him, and sidelining Madrid. This has led some in the party to question the entire leadership procedure in the party which means that if Aguirre wanted to make a formal challenge she would first have to assemble the support of 600 members of the party’s executive, 20% of the total. That could prove difficult for Aguirre given that Madrid has only 208 such votes.

Mariano Rajoy is reported to have threatened Aguirre with him choosing her arch-enemy, the Mayor of Madrid, Alberto Ruiz-Gallardón, possibly as party General Secretary, if she challenges him.

Meanwhile a new web called www.gallardon2012.com has been established with the intention of supporting the idea that the Mayor of Madrid runs for the leadership of the Partido Popular.
The web has been created by a group of party members who say that the party must change and adapt to the reality. They say the Mayor of Madrid is capable of that and his singular charisma could take the party to govern Spain again.