Nonsense. The Democrats have their own bill that they would be pleased to vote on. Now as to how palatable it would be to the President or the Republicans.
Republicans must get rid of the stupid Filibuster Rule,
That presupposes that McConnell could get 50 Republicans to vote for whatever immigration bill gets out of the House. Not a done deal.
The democrats will take a bipartisan bill similar to the bipartisan bill in 2006 and/or 2013.
Both of the bills passed out of senate with 63-64 cloture votes but never got a vote in the House because of the Hastert rule, even though there were enough votes on the floor of the House to pass.
This exercise of the GOP trying to compromise a bill out of the House is because they don't want to invoke the Hastert Rule again. Both Hastert and Boehner invoked Hastert but Ryan doesn't want to because it will hurt his reputation
In just a few days the senate as it is made up could pass a bipartisan bill that would have enough votes on the floor of the House to pass.
Immigration is the prerogative of the Senate.