NEW YORK — The day started with congressional leaders trying to resolve the dangerous impasse over the debt ceiling — and calm any anxiety markets may have when they reopened Monday.

It ended in a continuing impasse, with each party sketching out their own plans and showing little common ground.

Senate Majority Leader Harry Reid said he is preparing a proposal to raise the ceiling through the end of 2012 and cut $2.7 trillion in debt. The measure would not call for any tax revenue increases.

On the other side, House Speaker John Boehner told GOP lawmakers Sunday in a conference call that he wants a deal that sticks to the principles of the Cut, Cap and Balance bill that the House passed and Senate rejected last week.

A key sticking point remains how much to raise the debt ceiling: Democrats want it raised enough so the issue won’t come up again until after the November 2012 election. Boehner has said that is impossible; he wants it raised in two, smaller increments.

If Congress fails to act, the Treasury Department has said that on Aug. 2 it will run out of the cash it needs to pay all of the federal government’s bills on time.