WASHINGTON (CNN) -

If nothing else, the latest ISIS act of barbarism brought a quick political consensus, and added pressure on President Barack Obama: Caution in the face of repugnant horror just won't do.

The president responded Wednesday in his first public remarks since the beheading of journalist Steven Sotloff. He promised results while pleading for time to deal with Islamic terrorists in Iraq and Syria.

"Our objective is clear: That is to degrade and destroy ISIL so it's no longer a threat," " Obama said during a news conference in his trip to Estonia.

"It's going to take some time, it's going to take some effort," he said.

His comments came the day after lawmakers from both sides of the aisle called for action.

"We must use every tool at our disposal, short of introducing ground forces in combat roles, to put an end to the threat they pose to our national security," Democratic Sen. Jeanne Shaheen of New Hampshire said in a statement Tuesday.

Florida GOP Sen. Marco Rubio, rarely on the same page as Shaheen, also called on Obama to respond, and quickly.

"There is no disease that becomes easier to treat the longer you wait," Rubio said.

But whether increased bipartisan pressure will translate into a dramatically new and bolder administration approach is an open question.

"He is not going to plunge America into another trillion-dollar social science project because two American journalists have been killed, no matter how horrific it is," said longtime State Department hand Aaron David Miller, now a scholar at the Wilson Center.

Still, given the second barbaric beheading in a few weeks and the growing political calls for more decisive action, Miller said, "You can't imagine him not responding in some way."

The rush of statements from politicians shared similar language calling for action and a better explanation of U.S. policy.

'Let there be no doubt, we must go after ISIS right away," said Democratic Sen. Bill Nelson of Florida, the senior senator from the home state of American journalist Steven Sotloff.

"It is long overdue for the Obama administration to present to the Congress, the American people, and our allies around the world a comprehensive strategy to respond to the horrific threat ISIS poses," moderate GOP Sen. Susan Collins said in a statement.

And Sen. Lindsey Graham of South Carolina, already among the Republicans suggesting Obama has been too timid in responding to the ISIS threat, said it was time to stop debating whether to use U.S. air power against ISIS leadership targets in Syria.

"Condemnation is not enough to deal with this scourge. It is time we act decisively," Graham said. The GOP hawk said airpower had proven to be effective against ISIS targets on a limited basis in Iraq and said now: "It's a tactic that should be aggressively pursued both in Syria and Iraq. Mr. President, if you can't come up with a strategy, at least tell us what the goal is."

The timing also adds to the pressure on the President.

ISIS released the video showing the purported murder of Sotloff as Obama traveled to Europe to attend a NATO summit, where responding to ISIS is a top agenda item.

Miller sees sad irony in the fact that a president who made a name for himself in politics with innovative uses of social media to communicate "is now forced to respond because of this cruel and savage use of it."

As the commander in chief traveled, a top State Department official urged patience even in the wake of the apparent Sotloff beheading.

"Obviously, ISIS is a very sophisticated organization," Deputy Assistant Secretary of State Brett McGurk told CNN's Christiane Amanpour. "You cannot just go in militarily and start dropping bombs, and hope that it's going to work out. You have to have a very sophisticated approach to this."

In the short term, veteran diplomats and intelligence experts acknowledge the pressure on the White House to respond with force will be intense, but they cautioned the menu of options might not be terribly appealing.

"I'm not sure there is a one-off airstrike or small set of airstrikes that would achieve much right now," Miller said. "And I don't think they are ready, in terms of identifying the targets, for a sustained and comprehensive set of strikes in Syria right now."

Given that the options are hardly appealing, Miller said the President's often-criticized caution makes considerable policy sense. "But his risk aversion is politically a disaster for him."

While mulling new military and diplomatic moves, Miller and others suggested a growing urgency for the president to set a speech or some other event to explain in detail the ISIS threat and his deliberations.