Senate Republicans and immigration activists alike wasted little time in panning a new border security initiative announced Tuesday by the White House that would send 1,200 National Guard troops to the Mexican border.

While Senate Republicans accused the administration of doing too little to control violence, drug smuggling and human trafficking along the border, activists slammed the White House for “rewarding” Republicans who have resisted efforts to pass an immigration overhaul.

Arguing that President Barack Obama must be “personally committed to ending illegality at the border,” Senate Judiciary ranking member Jeff Sessions said the new troops are only a temporary solution.

“Announcing and taking specific steps can be helpful, but only if it’s part of a determined and consistent effort to fix the problem. The president’s decision to send up to 1,200 troops to the border, while helpful, will not fix the problem,” the Alabama Republican said.

Sessions also attacked the administration on the issue in general, denouncing its criticism of a tough new immigration law in Arizona and complaining that “members of President Obama’s administration gave Mexican President Felipe Calderón a standing ovation as Calderón proceeded to slander the state of Arizona for its efforts to protect its citizens.”

National Republican Senatorial Committee Chairman John Cornyn (Texas) also panned the administration’s proposal.

“While I appreciate the president’s acknowledgment that his administration has done too little to secure our border, his proposal still comes up short. Temporary fixes are no solution to long-term challenges,” Cornyn said.

Obama even took fire from supporters of a comprehensive immigration overhaul, who complained that the White House was selling out immigrants in the hopes of attracting GOP support.

Frank Sharry, executive director of America’s Voice, accused the White House of “giving in” to Arizona GOP Sens. John McCain and Jon Kyl, both of whom have repeatedly called for added troops along the border.

“Giving in to McCain and Kyl on immigration sure has the same feel as when the administration caved and excluded unauthorized immigrants from the health care exchange following Rep. Joe Wilson’s (R-S.C.) rude outburst last year during the president’s joint address to the Congress. It has the feel of the president’s recent embrace of offshore drilling, just weeks before the BP disaster struck. Give them what they want and hope they’ll play nice,” Sharry said.

But if Obama’s aim was to win over McCain, it clearly wasn’t working — as the Arizona Republican on Tuesday called the proposal “simply not enough.”

Obama did have some supporters, at least among House Democrats, including several from Texas.

“We commend the president in making this supplemental request to augment federal, state and local law enforcement working to secure the nation’s southern border,” reads a statement by Democratic Reps. Henry Cuellar, Charles Gonzalez, Rubén Hinojosa, Solomon Ortiz and Silvestre Reyes, all of whom represent border districts in Texas.

The Texas lawmakers noted that they recently joined with lawmakers in California, Arizona and New Mexico to request $500 million in emergency funds to help beef up law enforcement at the border in response to reports of escalating violence in Mexico.

“We look forward to working with the White House as more information becomes available as to where and when these additional border security resources will be deployed,” they said.

Jennifer Bendery contributed to this report.