Republicans squabble over who has lead role in fight to stop ObamaCare

Tensions are rising between House and Senate Republicans over which conference will lead the fight to defund ObamaCare.

Sen. Ted CruzTed CruzIs Georgia turning blue? Five takeaways from money race Club for Growth: Anti-Trump spending proved to be 'good call' MORE (R-Texas) and a spokesman for Speaker John BoehnerJohn BoehnerTrump may pose problem for Ryan in Speaker vote Conservatives backing Trump keep focus on Supreme Court Vote House Republicans out MORE (R-Ohio) each said Wednesday that the task is for Republicans in the other chamber as pressure rises to fund the government.

Cruz's statement drew immediate criticism from rank-and-file House Republicans who accused the likely presidential hopeful of abandoning the fight he had encouraged for months. 

"So far [Senate Republicans] are good at getting Facebook likes, and townhalls, not much else. Do something …" tweeted Rep. Tim GriffinTim GriffinTea Party class reassesses record Huckabee's daughter to run '16 campaign Lawmakers seek Purple Heart for victims of Little Rock shooting MORE (R-Ark.).

The rift highlights the desire by GOP lawmakers to avoid blame for any shutdown that occurs because of demands to kill ObamaCare.

Cruz and his allies — Sens. Marco RubioMarco RubioRubio: GOP Congress could go in different direction than Trump Poll: Clinton holds 4-point lead in Florida Republicans, it's time to stop asking 'What would Reagan do?' MORE (R-Fla.) and Mike LeeMike LeeDonald Trump's Mormon PR problem Trump's big worry isn't rigged elections, it's GOP establishment GOP senators avoid Trump questions on rigged election MORE (R-Utah) — campaigned throughout the month of August for aggressive tactics against ObamaCare in the fight to fund the government.

House GOP leaders appeared unwilling to follow this strategy until Wednesday, when they announced they would strip out money for the healthcare law in a stopgap continuing resolution (CR).

The plan would hand the fight to conservative senators, who would presumably work to gather votes against funding ObamaCare or perhaps filibuster a Democratic spending bill.

Cruz, Rubio and Lee praised the House GOP's strategy for its boldness, but in a statement, Cruz waved off expectations that he prevail in the Senate fight.

"[Senate Majority Leader] Harry ReidHarry ReidPelosi blasts GOP leaders for silence on Trump Latinos build a wall between Trump and White House in new ad The true (and incredible) story of Hill staffers on the industry payroll MORE will no doubt try to strip the defund language from the continuing resolution, and right now he likely has the votes to do so," Cruz said.

"At that point, House Republicans must stand firm, hold their ground, and continue to listen to the American people."

BoehnerJohn BoehnerTrump may pose problem for Ryan in Speaker vote Conservatives backing Trump keep focus on Supreme Court Vote House Republicans out MORE spokesman Michael Steel responded in a statement insisting that Senate Republicans own the battle. "We trust Republicans in the Senate will put up a fight worthy of the challenge that ObamaCare poses," Steel said.

Senate Democrats and President Obama are unified in their opposition to any spending bill that undercuts healthcare reform.

Republicans are hoping that, in the face of a shutdown on Oct. 1, Obama blinks and allows the GOP to defund his signature law. 

As of Wednesday evening, criticism from House Republicans against Cruz was building on Twitter. In one posting, Rep. Sean DuffySean DuffyDistrict Court right to target CFPB Tech groups file court brief opposing internet transition suit Yellen defends Fed from Trump attacks MORE (R-Wis.) accused Cruz and Lee of "refusing to fight."

"House agrees to send CR to Senate that defunds ObamaCare. Sen. Ted Cruz and Sen. Mike Lee … wave white flag and surrender," Duffy tweeted.