Sen. Lindsey Graham on Wednesday boasted of "growing momentum" among GOP senators for a bipartisan immigration deal on Capitol Hill, despite pushback from the White House.

A press release from the South Carolina Republican's office announced Sens. Susan Collins, R-Maine; Lamar Alexander, R-Tenn.; Lisa Murkowski, R-Alaska; and Mike Rounds, R-S.D., have all indicated support for the proposal that would offer a solution for the Deferred Action for Childhood Arrivals program, which protects illegal immigrants brought to the U.S. as children. They join Jeff Flake, R-Ariz., and Corey Gardner, R-Colo., who already support the deal.

“I’m very pleased that our bipartisan proposal continues to gain support among my Republican colleagues,” Graham said.

Some highlights of the proposed plan include an abolishment of the current diversity visa lottery system, additional border security measures, and a 10-year waiting period for "Dreamers" to gain citizenship.

The bipartisan deal was devised in part by a contingent of Democrats too, led by Minority Whip Dick Durbin, D-Ill. While those spearheading the bipartisan effort are seeing a rising number of supporters, passage of the bill is not guaranteed if it is not supported by enough Democrats or Senate Majority Leader Mitch McConnell, R-Ky., who indicated he would not bring a bill to a vote on the floor if it doesn't have the support of the White House — which this bipartisan effort does not yet have.

Meanwhile, Sens. Chuck Grassley, R-Iowa; Tom Cotton, R- Ark.; and David Perdue, R-Ga., put out a joint statement expressing their concerns over the bipartisan immigration proposal.

"The Durbin-Graham-Flake proposal would do nothing to solve the underlying problem in our current immigration system,” the statement said. “It does not take the needed steps to fix our porous border and it fails to empower law enforcement to apprehend and remove dangerous criminals who are here illegally.”

The Republicans in opposition to the bipartisan deal join President Trump who has called the plan “very, very weak.”

Lawmakers are working to find a solution on DACA, which expires on March 5, and immigration amid a looming government shutdown.