The House will consider a replacement to No Child Left Behind, while the Senate continues debate on DHS funding.
The New Jersey Democrat said the administration should also provide more assistance to Ukraine's military.
Speaker Boehner halted floor proceedings to remind members of chamber decorum.
The Michigan Democrat said if House lawmakers don't pass a "clean" DHS spending bill "they are putting in place a shutdown."
The bill passed 401-20.
"If you don't do your job, you shouldn't get paid," Rep. Ashford said.
The unanimous consent requests failed on the floor.
Rep. Carney's (D-Del.) call comes ahead of the 50th anniversary of "Bloody Sunday."
The senator said Obama "doesn't understand the mistakes he's been making."