BY RAFAEL BERNAL - 10/13/17 01:35 PM EDT

The ranking Democrats on six House committees are asking Speaker Paul Ryan (R-Wisc.) to channel through their panels a bill that seeks to spend $10 billion on President Trump’s proposed border wall.

The bill, cleared by the House Homeland Security Committee on a party-line vote last week, was originally proposed by that committee's chairman, Rep. Michael McCaul (R-Texas).

Now ranking members from the Natural Resources, Armed Services, Transportation and Infrastructure, Ways and Means, Oversight and Government Reform and Foreign Affairs committees want the opportunity to mark up the legislation before it heads to the House floor.

In a letter to Ryan and each committee’s chair, signed by Democratic Reps. Raúl M. Grijalva (Ariz.), Adam Smith (Wash.), Peter DeFazio (Ore.), Richard Neal (Mass.), Elijah Cummings (Md.) and Eliot Engel (N.Y.), the lawmakers quoted Homeland Security ranking member Rep. Bennie Thompson (D-Miss.), calling the bill "a misguided, unnecessary, fiscally-irresponsible measure to formally authorize President Trump’s Wall at all costs.”

“We ask each Committee Chairman to assert his jurisdictional claim over the bill,” the Democrats said.

Democratic leadership has refused to budge toward Trump’s long-pledged Mexican border wall and has threatened to kill any legislation that funds it.

The bill in question, the Border Security for America Act, would also add $5 billion to improve security at U.S. ports and 5,000 agents to both the Border Patrol and Customs and Border Protection.

Democrats have been heavily critical of the bill, which they see as serving a double purpose: to appease Trump by granting border wall funding, and to provide a vehicle for a quid pro quo on a potential deal to protect Deferred Action for Childhood Arrival recipients from deportation.

In the bill's original Homeland Security Committee markup, all Republican amendments were approved and none of the Democratic proposals were cleared.

According to the ranking members of the committees in question, the House parliamentarian has ruled that the bill "includes provisions relevant to each of the committees’ jurisdictions."