"The border is not secure; that is a simple fact," McCaul said as his panel approved a limited border bill last week.
But even as the White House expressed its opposition to the plan, there were rumblings of discontent from within the GOP as well over how this effort on immigration would begin in the House, as Republican critics said the bill leaves too much unaddressed.
"It does not cut off access to federal welfare, when it should," argued Rep. Mo Brooks (R-AL). "It does not include any work site enforcement, when it should."
"In effect, it does nothing to reduce the incentives for illegal aliens to come to America," Brooks added to reporters, as he rattled off a list of grievances after a closed door GOP meeting last week.
Dissenting views were also heard from Republicans in the Senate.
"Republicans won a historic midterm vote on the promise to take real action—not symbolic gestures—to end the immigration lawlessness," said Sen. Jeff Sessions (R-AL).
If those are just a few voices, GOP leaders should be fine this week, but - if those numbers grown - it could turn into a repeat of last week in the House, when a pro-life bill on late term abortion had to be shelved after a rebellion led by women lawmakers and more moderate GOP members.
While that abortion dispute was embarrassing for top Republicans - failure this week on a border security bill might be much worse, raising fresh questions about the reluctance of rank-and-file Republicans to rally behind their leaders.
Leading Republicans say this bill was never meant to do everything on immigration - and that GOP leaders have long talked about splitting up various issues among a series of bills.
One Republican lawmaker described to me his lobbying session with a newer member of Congress, who was ticking off a list of things the bill didn't do, as it became clear that GOP lawmaker wasn't on board with a peacemeal approach.
"The Homeland Security Committee doesn't have the jurisdiction to do all those things," the frustrated GOP veteran told me, shaking his head at the reluctance of his colleagues to back this border plan.
The immigration plan is set to go before the House Rules Committee on Monday; a vote is set for Wednesday in the full House - if Republicans have the votes to approve the plan.
** UPDATE ** Because of the big winter storm in the northeast, the House delayed votes on Monday until Tuesday - and GOP leaders have taken the border security bill off the schedule for this week.
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