The House’s latest attempt is passing several “piecemeal” measures to fund national parks, the National Guard, veterans programs and the National Institutes of Health, among other things. But Senate Democrats have refused to take those up, saying the entire government needs to be reopened.

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“Chuck E. Cheese calls it Whac-A-Mole,” Durbin said Wednesday referring to the family-fun chain. “That’s what they’re doing in the House.”

The House was voting Wednesday on two more mini-spending bills on military death benefits and Federal Aviation Administration funding.

Senate Minority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellSessions: 'We should be like Canada' in how we take in immigrants NSA spying program overcomes key Senate hurdle Overnight Finance: Lawmakers see shutdown odds rising | Trump calls for looser rules for bank loans | Consumer bureau moves to revise payday lending rule | Trump warns China on trade deficit MORE (R-Ky.) and other Republicans have attempted to call up the House measures numerous times, but Democrats continue to object.

"We have offered 13 different compromises today to reopen the government," Sen. Rand PaulRandal (Rand) Howard PaulNSA spying program overcomes key Senate hurdle Fix what we’ve got and make Medicare right this year Despite amnesty, DACA bill favors American wage-earners MORE (R-Ky.) said. "Why don’t we open the parts of government that we agree to."

It's unclear where the fight will go from here as each side becomes more entrenched.