(CNN) Republicans are on the verge of their second high-stakes votes this week that will test their allegiance to President Donald Trump and force the party to reckon with how far it is willing to let executive power reach.

The votes -- first a resolution passed Wednesday that pulls back American aid to Saudi forces in Yemen , followed by a resolution Thursday to block Trump's emergency declaration on the southern border -- have left some in the GOP conflicted about whether they will vote with Trump or protect congressional authority on some of the biggest issues facing the Congress: war and government spending.

The resolutions are both privileged, which means they cannot be stopped by Senate Majority Leader Mitch McConnell, a Republican from Kentucky. And the votes come as the GOP has spent weeks debating how to soften their blow.

Republicans' hopes all but evaporated Wednesday afternoon after Trump called into the Republican Senate lunch to announce he would not support a proposal from GOP Sens. Mike Lee of Utah and Thom Tillis of North Carolina that would limit the President's future ability to issue national emergencies. The proposal from had been intended to try to limit the number of Republican defections on the national emergency vote Thursday.

For weeks, Republican senators have been working behind the scenes to try to convince the White House to use other means to build the President's border wall, including trying to draft a resolution that would have encouraged the White House to find money for the wall through less controversial appropriations transfers rather than the emergency declaration.

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