Your stored procedure should be working fine. The code below is working on my system.
use AdventureWorks2008R2;
go
create PROC [dbo].[sp_getrecords]
(
@TableName varchar(4000)
)
AS
begin
exec('select * from '+@TableName+'')
end;
go
exec [sp_getrecords] 'DatabaseLog';
exec [sp_getrecords] 'HumanResources.Department';