I don't know how important this is for the CDU. The political situation in Germany is a bit hard to read at the moment, but basically Merkel has lost a lot of her power internally to the 'Minister Presidents' of the German States. Or maybe she never had much. But anyway, they sort of blocked the drive for a reform of the health system and since then her standing has been diminished.

A couple of tidbits:

The 'Gottesbezug' was a common demand of the CDU and the CSU at the time when the convention was finished and the haggling at the European Council over the Constitution about to begin. So, they lost out there.

The MFA of Germany (Steinmeier) is from the SPD. This means that within the CDU, the people who have to worry most about the consequences of what Merkel says (besides Merkel herself) are the leaders of the Parliamentary Committees on the EU and Foreign Affairs.

I would guess that the call for this reference from God is mainly coming from the (more catholic) CSU and its leader, Stoiber. But it's also quite possible that it's simply Merkel who feels strongly about it.