''The president's veto of the Keystone jobs bill is a national embarrassment,'' said the top Republican in the House of Representatives, John Boehner.
''We are not going to give up in our efforts to get this pipeline built — not even close.''
The issue is about to play out on two fronts. One is a major presidential regulatory decision and the other, as suggested by Boehner, likely involves future clashes with Congress.
The Canadian government echoed that theme: ''It is not a question of if this project will be approved; it is a matter of when,'' said a statement from Natural Resources Minister Greg Rickford.
''We will continue to strongly advocate for this job-creating project.''
Even the White House concurred that the issue is far from settled. It pointed out that Tuesday's announcement was a step in a long, winding process — not a final destination.
The president cast the veto as a matter of procedural principle. In his letter to Congress, Obama said the bill he was scrapping had improperly tried to usurp presidential authority.
The White House position is that cross-border pipeline permits are a matter for the president to decide — not Congress, which passed a bill earlier this month forcing the approval of the project.
That bill was delivered to the president Tuesday and he vetoed it on the very first available day.
White House spokesman Josh Earnest said the president could still, in theory, approve the pipeline. The veto doesn't necessarily reflect Obama's view on the pipeline itself, he noted.
''It certainly is possible,'' Earnest said, noting the president would keep an "open mind" on the project.
"(This) does not represent a specific position on the pipeline itself... It just merely says that the benefits, and consequences, of building that pipeline should be thoroughly evaluated by experts and through this administrative process that has existed for decades.''
The administration is in the final phase of its regulatory review of the project — which was delayed by a dispute over the route in Nebraska, then again in a procedural dispute with Republicans in Congress in 2011, and once more during a court case involving Nebraska landowners last year.
The administration couldn't say Tuesday when the process would wrap up. But Earnest said he expects a decision soon after the conclusion of the review by the State Department, which is leading the process.
There could also be many more twists and turns in Congress, as alluded to by Boehner.
Republicans will attempt to override the veto, although they don't appear to have the necessary two-thirds majority. The project only has support from a minority of Democrats.
One of those rare Democrats also hinted at future congressional efforts. There's widespread expectation that lawmakers might try attaching a pipeline provision to legislation Obama might find attractive, and difficult to veto.
''We're going to basically find a middle, if you will, and move forward,'' West Virginia Democrat Joe Manchin told Fox News on Tuesday.
But the sides in this dispute can't agree on much else — not even basic poll findings.
Keystone XL supporters point to surveys consistently showing that a majority of Americans — or at least a plurality — support the project.
But environmentalists released their own poll this week suggesting most Americans don't really have a strong opinion on the issue, and would rather see Congress move on to other things.