"blanket support" is correct and usable in written English.
You can use it to refer to general, unconditional, or widespread support of an idea, cause, or person. For example: "The mayor received blanket support from the city council".
But the Tory position falls far short of blanket support for the government.
Governments of astonishing incompetence had for many years no policy other than the blanket support of a rapacious forestry industry run on scandalous subsidies.
"He took her support of his stance in the EU budget debate as a statement of blanket support for Britain's renegotiation strategy.
He expressed blanket support for the show and for his cast mates, saying only that "five years is a good amount of time".
It's good that they feel they have support – but they shouldn't feel it's blanket support such that they abrogate their own responsibility.
And yesterday's statement of blanket support for same-sex marriage by Democratic presidential hopeful Senator Russ Feingold has the blogosphere speculating on fallout.
"The blanket supports kangaroo care moments between mother and baby and is used as a supportive wrap that absorbs a mother's smell during kangaroo care.
These components include vacuum vessel ports, first wall, divertor private region, limiter and blanket supporting systems.
The VV support system has been improved, and the design of the VV shells and the blanket supports has been simplified.
It is necessary to make adjustments to the locations of the blanket supports and manifolds to accommodate design modifications to the in-vessel coils.
It was necessary to make adjustments in the locations of the blanket supports and manifolds to accommodate the design modifications in the ELM/VS coils.
