I thought about postingthis in the Politics SE but this is a legal question. In this article it appears that US Secretary of the Interior Ryan Zinke has explicitly told two legislators from Alaska that the way they cast their votes in the Senate have put federally funded projects planned for Alaska "in jeopardy". There are a lot of different ways this could be done, but ultimately it boils down to how the Secretary will/won't allocate funds for these projects.
The duty of the Legislative branch is to faithfully represent the people of their district/state when creating laws.
The duty of the Executive branch is to faithfully execute the laws that the Legislature creates when implementing programs.
The Founders designed it so that the Legislative branch would control the "Power of the Purse" as one of its checks & balances versus the Executive branch, yet here it seems that an Executive branch department is saying it will control the purse unless Legislature does what the Executive wants.
This seems to me to be a violation of the Separations of Powers at the very least but it also sounds like extortion or bribery for congressional votes. Another issue is that this kind of financial/political arm twisting essentially tries to force the legislators into representing the interests of the Executive over the interests of their constituents.
I do realize that political backroom deals for pork barrel spending and earmarked projects are also subject to the same arguments, but in those cases the process is much more visible and the entire Congress has a final voice in approving the specific allocations.