ring/sound hollow - if something someone says rings hollow, it does not sound true or sincere.

In view of the government's financial problems, these promises have a hollow ring.

• have a few irons in the fire
• have a few strings to bow
• have a few strings to your bow
• have a field day
• have a fighting chance
• have a [fine/good etc.] pair of lungs
• have a fine pair of lungs
• have a finger in every pie
• have a finger in the pie
• have a finger on the button
• have a fit
• have a foot in both camps
• have a free hand
• have a frog in throat
• have a frog in your throat
• have a good head on shoulders
• have a good head on your shoulders
• have a good mind
• have a good mind to do something
• have a good pair of lungs
• have a good run
• have a good run for money
• have a good run for your money
• have a good thing going
• have a grip on