Because the situation had changed drastically since Amidala went gone into hiding. No longer were the Federation simply looking to break away from the Republic, the information they'd gleaned on Geonosis (courtesy of Obi-Wan) suggested that the Separatists were building a vast droid army capable of destroying the whole Republic.
The Opposition senators are called before the Chancellor and he lays out the situation to them:
The word had passed, from Obi-Wan to Yoda and the Jedi Council, and
now from them to the Chancellor and leaders of the Senate, that the
Republic was crumbling. The mood inside Chancellor Palpatine’s office
was both somber and frantic, everyone overwhelmed by a sense of
despair and a need to act, frustrated by the apparent lack of options.
Yoda, Mace Windu, and Ki-Adi-Mundi represented the Jedi, lending an
air of calm against the nervous energy of Senators Bail Organa and Ask
Aak, and Representative Jar Jar Binks. Behind his great desk,
Palpatine listened to it all with apparent despair, his aide, Mas
Amedda, standing beside him, seeming on the verge of tears. Star Wars : Attack of the Clones - Official Novelization
The opposition are no longer opposing the granting of extra powers to the Chancellor, nor are they against the idea that Palpatine (as a former Naboobian Senator) would have anything other than the best of democratic intentions, to use the Army to protect the Republic from outside invasion:
“Unfortunately, the debate is not over,” Bail Organa said. “The Senate
will never approve the use of the army before the separatists attack.
And by then, it will likely be too late.”
“This is a crisis,” Mas Amedda dared interject. “The Senate must vote
the Chancellor emergency powers! He could then approve the use of the
Palpatine rocked back at the suggestion, seeming profoundly shaken.
“But what Senator would have the courage to propose such a radical
amendment?” he asked hesitantly.
“I will!” Ask Aak declared.
Beside him, Bail Organa gave a helpless chuckle and shook his head.
“They will not listen to you, I fear. Nor to me,” he added quickly,
when Ask Aak snapped a glare at him. “We have spent too much of our
political capital debating the philosophies of the separatists and
arguing for action. The Senate will not see our call as anything more
than overly alarmist. We need a voice of reason, one willing to
reverse position, even, given the gravity of the current situation.”
“If only Senator Amidala was here,” Mas Amedda reasoned.
Without hesitation, Jar Jar Binks stepped forward again. “Mesa mosto
Supreme Chancellor,” the Gungan said, squaring his sloping shoulders
as much as possible. “Mesa gusto pallos,” he said deferentially to all
the others. “Mesa proud to proposing the motion to give Yousa Honor
Palpatine looked from the trembling Gungan to Bail Organa. “He speaks
for Amidala,” the Senator from Alderaan said. “By all understanding
within the Senate, Jar Jar Binks’s words are a reflection of Senator
Amidala’s desires.” Star Wars : Attack of the Clones - Official Novelization