It’s unclear how serious a move this is. If the GOP really already had their shit together on acting as a bloc, this would be coming from McConnell, not Graham.
In fact, it’s possible to see this as a shrewd courtier’s tactic by Graham, even if he doesn’t get any signatures. It would be stupid for a GOP Senator to sign such a thing at this point, because they don’t yet know what new godawful shit about Ukraine may be exposed by the inquiry. Rather than commit, they can easily kick the can down the road by saying they’re waiting for the full articles of impeachment.
So Graham’s effort may not see much in terms of results. But he can scuttle back to Trump, hold up his petition as evidence he’s a good little ass-licking sycophant, denounce the Senators who wouldn’t sign, and build his capital with Trump.
Then if it looks like Trump is going down, he can blame the Senators who didn’t sign to keep cred with Trump supporters, and flip using the “It’s clear the Administration can’t continue if his own party doesn’t support him” card.
… Of course, a way simpler and more likely explanation is that Graham really is just an ass-kissing sycophant.