"I think most people understand that you're not in a position to stop Senator Cruz from pursuing the issues he wants to pursue," said a lobbyist who consults with the oil industry and is familiar with the flurry of lobbying activity the amendment set off. "Cruz will certainly follow the force of his conviction."
"[Lifting the ban] is good, pro-growth policy, which is why he has taken the opportunity to file the measure as an amendment to the Keystone bill, just like many other senators have offered amendments with their own priorities. We look forward to seeing how the legislative process plays out," Frazier said Thursday.
Several advocates working to lift the ban also said that the industry does not want debate on crude exports to come up in the midst of a Keystone XL vote, out of fear that the highly-charged politics of the pipeline could rub off on exports.
"What you don't want is for this to get sucked up into a much larger and potentially toxic debate on Keystone and for positions to get entrenched early on," the lobbyist said.
Senate leadership has declined to offer full-throated support for the amendment. Leadership has final say over which amendments will be considered. And so far, Senate Majority Leader Mitch McConnell has said he won't block any amendments.
McConnell has not yet said if he supports lifting the ban on oil exports, and his office declined to answer whether he would support the Cruz amendment.
Robert Dillon, a spokesman for Senate Energy and Natural Resources Committee Chairwoman Lisa Murkowski, one of the most outspoken backers of lifting the ban, would say only that Murkowski "welcomes Senator Cruz's support on this issue." Dillon declined to say how Murkowski would vote.
An aide to Senate Majority Whip John Cornyn of Texas, who has also expressed support for lifting the ban, would not indicate if the senator had decided how he would vote.
It's unclear if Cruz will call for debate on the amendment or a vote. Cruz could opt to do neither, or the senator could press for debate but table the proposal prior to a vote.
If the amendment is voted down, lobbyists plan to continue marshalling evidence to make their case that the ban should be lifted, and they are optimistic that as more research emerges they will be armed and ready to convince senators to change their minds and votes.
Regardless of what happens with the Cruz amendment, hearings on lifting the export ban are expected to be held in Murkowski's committee, and lobbyists are hoping that a measure to lift the ban could be attached to broader energy legislation that she has said she is working to draft.
"This issue is going to be around for a while no matter how you slice it," the refinery executive said. "I think we might see a lot of shadowboxing in the next few weeks, but I believe the real fight is still to come."
This story has been updated with additional information.
Ben Geman contributed to this article