Republicans are expected to try passing several bills to make up for funding gaps caused by the shutdown. Aside from Veterans Affairs, the GOP will also pursue bills to fund national parks and the local Washington, D.C., government.

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These bills are expected to be called up under a suspension of House rules, which would require Democrats to support them if they're going to pass.

"House Republicans rightly acted four times to avoid a government shutdown and protect Americans from the harmful effects of ObamaCare," Salmon said Tuesday. "While Senator Harry ReidHarry ReidSanders and Schumer are right: Ellison for DNC chair The Hill's 12:30 Report Hopes rise for law to expand access to experimental drugs MORE continues to refuse to come to the table, this bill makes sure our veterans are taken care of while Congress works to hammer out a final bill."

An aide to Salmon said there are more than 40 co-sponsors of his bill, which was just introduced shortly after noon today.

The bill is similar to legislation offered by Sen. Ted CruzTed CruzBrietbart CEO reveals that Trump donors are part owners At CPAC, Trump lashes out at media Conquering Trump returns to conservative summit MORE (R-Texas) in the Senate. Cruz has pushed for Republicans to seek smaller funding bills in response to the shutdown.

Tuesday afternoon, White House spokesman Jay Carney said passing several smaller bills would not be a "serious" way to address the shutdown.