US senators will begin a series of votes on Wednesday to authorise a 90-day window for US military action against Syria, as the Obama administration's campaign to win over sceptics in Congress gained momentum.

A new draft resolution was agreed by leaders of the Senate foreign relations committee after secretary of state John Kerry pressed a forceful case for striking against the Assad regime. Earlier, Barack Obama secured the backing of the Republican leadership at a key White House meeting.

The president headed for Europe on Tuesday night for what promised to be a testy meeting of the G20 group of industrialised nations. After a short visit to Sweden, Obama will travel to St Petersburg in Russia where the host of the G20, Vladimir Putin, is likely to give the US a rough ride over its plans for air strikes against Syria.

In Washington, key members of Congress swung behind the administration on Tuesday. At the senate foreign relations committee, Kerry and the defence secretary Chuck Hagel were pressed hard to clarify the role of ground forces, but got an otherwise sympathetic reception.

In the evening, details emerged of the committee's revisions to a the White House's proposals for a military authorisation. They set a window limited to 60 days for military action – during which Obama could order the limited, tailored strikes he has foreshadowed – while allowing for a single 30-day extension subject to conditions. Democrat committee chairman Bob Menendez and his Republican counterpart Bob Corker also added a provision banning any use of US armed forces on the ground in Syria.

Committee members are now expected to begin "marking up" the resolution – voting on specific amendments – following a further classified briefing on Wednesday morning. The House of Representatives, where Obama is likely to get a rougher ride, begins its deliberations with a public hearing on Wednesday. Full votes before the Senate and House are expected on Monday.

Sceptical Republicans appeared to have been won over by tougher rhetoric from the White House. For the first time, Obama portrayed his plans for US military action in Syria as part of a broader strategy to topple Bashar al-Assad. While stressing that Washington's primary goal remained "limited and proportional" attacks to degrade Syria's chemical weapons capabilities and deter their future use, the president hinted at a long-term mission that may ultimately bring about a change of regime.

"It also fits into a broader strategy that can bring about over time the kind of strengthening of the opposition and the diplomatic, economic and political pressure required – so that ultimately we have a transition that can bring peace and stability, not only to Syria but to the region," Obama told senior members of Congress at a White House meeting earlier on Tuesday.

The president has long spoken of the US desire to see Assad step down, but this was the first time he has linked that policy objective to his threatened military strikes against Syria. It follows pressure on Monday, from senators John McCain and Lindsey Graham, to make such a goal more explicit.

The apparent change of emphasis appeared to resolve some of the political deadlock on Capitol Hill, as House speaker John Boehner and a series of other Republican leaders announced they would back the president's call for military authorisation from Congress.

The endorsement of GOP leaders could be important in winning over the Republican-controlled House, where Obama has failed to win any support since his re-election in November. But even the Republican leadership has struggled to control Tea Party radicals in the House, and an anti-interventionist wing in the Senate led by Rand Paul remains a substantial challenge for the White House.

"I'm going to support the president's call for action, and I believe my colleagues should support the president's call for action," Boehner said after meeting the president at the White House. "The use of these weapons has to be responded to, and only the United States has the capability and the capacity to stop Assad and to warn others around the world that this type of behaviour is not to be tolerated."

So far, the tougher US rhetoric does not seem to have deterred Democrats who back the president's call for military action on humanitarian grounds. Emerging from the White House meeting shortly after Boehner, House minority leader Nancy Pelosi said Syria's alleged used of chemical weapons was "outside the circle of acceptable human behaviour", but said she would not whip Democrats into voting yes.

"I don't think congressional authorisation is necessary, but I do think it is a good thing, and I think we can achieve it," she added.

For nearly three hours of the subsequent Senate committee hearing the only voices speaking against intervention were those of anti-war campaigners repeatedly ejected by security staff. When senators Rand Paul and Tom Udall eventually began more hostile questioning of Kerry, he brushed it off by asking them to consider what Syria's response might be to a US decision not to strike. "I guarantee you there would be further chemical attacks," Kerry told Paul.

The administration received crucial backing from chairman of the joint chiefs of staff, General Martin Dempsey, who had recently been openly sceptical of the merits of US military intervention. Dempsey said the evidence of alleged Syrian chemical weapons use had changed his mind.

But Kerry was forced to backtrack after appearing to acknowledge that US ground troops could become involved under certain scenarios. "In the event that Syria imploded, for instance, or in the event there was a threat of a chemical weapons cache falling into the hands of al-Nusra or someone else, and it was clearly in the interests of our allies, all of us, the British, the French and others, to prevent those weapons of mass destruction [falling into their hands]," Kerry said, "I don't want to take off the table an option that might or might not be available to the president."

Five times in subsequent exchanges the secretary insisted he had not meant to imply that "boots on the ground" was something actively planned by the administration. He faced hostile questioning from Republican hawk John McCain who asked why the administration was not going further in helping Syrian rebels overthrow Assad. But McCain made it clear he would vote in favour of a resolution to authorise military action.

With the chances of successful votes in Congress next week looking a little stronger, Obama will now head to Europe in the hope of persuading more world leaders to back his strategy.

President François Hollande of France called on Europe's leaders to unite over Syria, but hopes in Washington that Britain might hold a fresh parliamentary vote over joining military action were dashed on Monday, when prime minister David Cameron ruled out such a move.

The White House first announced that it would provide limited military support to Syrian rebel groups in June, but it has been criticised for dragging its heels over fears that arms might fall into the wrong hands.

The alleged chemical attacks by Assad forces now seem to have strengthened the hands of those in Washington who favour more direct assistance. The New York Times reported on Tuesday that CIA-trained rebels were now operating inside Syria.