Ellis said "essential" federal workers who stayed on the job "will feel like suckers because they've been working while the others essentially are getting paid vacations."
The White House has opposed other piecemeal efforts by House Republicans to restore money to some functions of government during the partial shutdown. White House officials have said the House should reopen the entire government and not pick agencies and programs over others.
In the 1995-96 government shutdowns, furloughed workers were retroactively given full pay.
Despite the White House's declared appreciation of the essential the role of federal workers, there appeared no sign of a breakthrough in getting them back to work.
Lawmakers keep replaying the same script on Capitol Hill: House Republicans pass piecemeal bills to reopen popular and politically sensitive programs — on Friday, disaster relief and food aid for the poor — while Democrats insist that the House vote on a straightforward Senate-passed measure to reopen all of government.
"We know that there are enough members in the House of Representatives — Democrats and Republicans — who are prepared to vote to reopen the government,' Obama said in an Associated Press interview Friday. "The only thing that is keeping that from happening is Speaker (John) Boehner has made a decision that he is going to hold out to see if he can get additional concessions from us."
There seemed little chance of that.
For one thing, flinching by either side on the shutdown might be seen as weakening one's hand in an even more important fight looming just over the horizon as the combatants in Washington increasingly shifted their focus to a midmonth deadline for averting a first-ever default.
"This isn't some damn game," Boehner, R-Ohio, said as the White House and Democrats held to their position of agreeing to negotiate only after the government is reopened and the $16.7 trillion debt limit raised.