With 306 seats in the House of Commons, David Cameron’s Conservatives are still 20 short of a bare majority. But if they are backed by the 57 legislators from third-place Liberal Democrats they would have a comfortable cushion for passing legislation.

Liberal Democrat leader Nick Clegg has said the Conservatives deserve a chance to try to form a government because they won the most seats in Thursday’s voting. The Liberal Democrats announced that their negotiating team would meet with the Conservatives at 1000 GMT on Sunday. A senior Liberal Democrat legislator suggested that Wednesday was the deadline for agreement.

One possible deal is a coalition government, in which the Liberal Democrats would take a few Cabinet posts. Or, the Liberal Democrats could strike a bargain to support a minority Conservative government on key issues. Any deal would require backing from three-fourths of Lib Dem legislators and the same proportion of its executive.

For the time being, Prime Minister Gordon Brown remains in office despite his Labour party’s second-place finish in the election.

Cameron and Clegg share views on the economy and could commit to a tough program of spending cuts aimed at reducing Britain’s record £153 billion ($236 billion) deficit. The pace of austerity measures would to be slower in a coalition than if Cameron had won a majority.

Clegg’s plan to cut taxes for the lowest-paid British workers would likely be taken up in a coalition government, and the partners could agree to scrap a planned rise in National Insurance — a payroll tax levied on employers and their staff.

They would likely agree to take quick action to scrap Britain’s planned national identity card program and reach accord on pushing allies harder for an international deal to reduce greenhouse gas emissions.

Though the two parties have wildly different views on foreign affairs, both are committed to keeping British troops in Afghanistan, at least in the short term. Clegg’s party describes itself as a “critical supporter” of the conflict, while Cameron has pledged a withdrawal of British forces within five years.

Both have signaled they may take a more skeptical tone in relations to the White House — Cameron previously attacked as “slavish” the links Tony Blair and Gordon Brown have shared with Washington.

The potential partners have major disagreements over Europe — Clegg’s party is in favor of Britain eventually joining the euro currency, a policy Cameron’s bloc bitterly opposes.

There could be tensions too on how to handle Iran’s nuclear program. The Liberal Democrats say they’ll support targeted sanctions but would not back military action.

A first major test of any alliance would be on Britain’s plan to replace its fleet of nuclear missile-carrying submarines. Clegg opposes the multi-billion plan for a new submarine fleet.

Simon Hughes, a senior Liberal Democrat legislator, said talks among the party’s legislators about the path forward would continue through the weekend.

“There won’t be a deal on the table because the talks have only just begun, but we will discuss where we want to go,” Hughes said in a BBC radio interview.

“Everybody in Britain will expect us to be responsible. We know what the timetable is, it’s between now and next Wednesday when Parliament comes back,” Hughes said.