CAIRO -- Protesters stormed onto the grounds of the Egyptian presidential palace Tuesday in a dramatic escalation of the crisis over President Mohammed Morsi’s decision to give himself absolute judicial power and set a quick referendum on a controversial new constitution.

Police made what appeared to be halfhearted efforts to confront the protesters, who commandeered a police vehicle as they approached the palace and painted graffiti on the palace walls. The inability, or unwillingness, of the police to keep Morsi opponents at bay raised questions about whether the nation’s last remaining arbiter, the military, would intervene in the dispute, and if so, on whose side.

Demonstrations also erupted in other parts of the country. In Alexandria, Egypt’s second largest city, protesters also stormed a presidential palace. In some areas, they vowed to stay the night.

Protesters gathered, as well, in front of the state building in Cairo that houses the government news service, where they beat drums, waved Egyptian flags and called for Morsi to go. “We won’t leave. He will leave,” the protesters chanted, recalling the 18 days of protests early last year that ended in the resignation of then-President Hosni Mubarak. Rusted barbed wire that had been laid out during the anti-Mubarak protests still ringed the building Tuesday.

The turn of events made it appear increasingly difficult for Morsi to ignore his opponents, who charge that the president, a top leader of the Muslim Brotherhood until his election in June, is grabbing power and manipulating events to empower the Brotherhood.

Opponents have said they want a president who’s more representative of the electorate and have demanded that Morsi rescind his declaration of immunity from judicial oversight. They also want him to cancel the constitutional referendum, set for Dec. 15, until a more representative constitutional assembly can produce a document. The current assembly is dominated by the Brotherhood after secular and Christian members withdrew.

In a televised interview late last week, Morsi said the proposed constitution would bring stability. But Tuesday’s protesters said that by pushing a document written by the Muslim Brotherhood-dominated constitutional assembly and rushing a referendum over the objections of some judges, Egypt was entering a period of persistent instability.

The constant threat of protests has paralyzed the capital, with Cairo’s bustling streets routinely empty on protest days.

Morsi also postponed until February a trip to Washington that had been planned for December, but his spokesman, Yasser Ali, denied that the delay was related to the protests.

The demonstration at the palace was one of two that opponents had scheduled Tuesday in Cairo. The other was in Tahrir Square, the epicenter of the anti-Mubarak protests nearly two years ago. At both protests, the crowds chanted “Leave!” and “Down, down with Morsi Mubarak.”

While the protests at Tahrir were relatively subdued, the crowds at the palace began taking down the barbed wire that had been strung Tuesday morning on the road leading to the palace. Police standing behind the wire fired a few rounds of tear gas in an effort to discourage the crowd, but before long they could be seen joking with the protesters. At times, it appeared that some officers had joined in.