The phrase "lukewarm support" means that someone is not fully enthusiastic or strongly supportive of something. They are only showing a mild or moderate level of support. Full definition
The Conservative party is offering lukewarm support for the legislation, despite the pledge being included in the 2010 coalition agreement. (politics.co.uk)
The announcement was met with lukewarm support by some. (timesunion.com)
I often work with couples who have experienced lukewarm support for their primary relationships in other forms of counseling or self help. (moderncommitment.com)